[1] J., Adámek, H., Herrlich, G., Strecker. Abstract and Concrete Categories–The Joy of Cats. John Wiley and Sons (1990), online edition available at http://katmat.math.uni-bremen.de/acc/.Google Scholar

[2] J., Adámek, J., Rosický. Locally Presentable and Accessible Categories. LONDON MATH. SOC. LECTURE NOTE SERIES 189, Cambridge University Press (1994).Google Scholar

[3] J., Adams. Infinite Loop Spaces. ANNALS OF MATH. STUDIES 90, Princeton University Press (1978).Google Scholar

[4] M., Artin. Versal deformations and algebraic stacks, Invent. Math. 27 (1974), 165–189.Google Scholar

[5] D., Ara. Sur les ∞-groupoïdes de Grothendieck et une variante ∞-catégorique. Doctoral thesis, Université de Paris 7 (2010).

[6] H., Bacard. Segal enriched categories I. Arxiv preprint arXiv:1009.3673 (2010).

[7] B., Badzioch. Algebraic theories in homotopy theory. Ann. Math. 155 (2002), 895–913.Google Scholar

[8] J., Baez, J., Dolan. Higher-dimensional algebra and topological quantum field theory. J. Math. Phys. 36 (1995), 6073–6105.Google Scholar

[9] J., Baez, J., Dolan. n-Categories, sketch of a definition. Letter to R. Street, 29 Nov. and 3 Dec. 1995. Available online at http://math.ucr.edu/home/baez/ncat.def.html.

[10] J., Baez. An introduction to n-categories. In Category Theory and Computer Science (Santa Margherita Ligure 1997). LECT. NOTES IN COMPUTER SCIENCE 1290, Springer-Verlag (1997), 1–33.Google Scholar

[11] J., Baez, J., Dolan. Higher-dimensional algebra III: n-categories and the algebra of opetopes. Adv. Math. 135 (1998), 145–206.Google Scholar

[12] J., Baez, J., Dolan. Categorification. In Higher Category Theory (Evanston, 1997). CONTEMP. MATH. 230, A.M.S. (1998), 1–36.Google Scholar

[13] J., Baez, P., May. Towards Higher Categories. IMA VOLUMES MATH. APPL. 152, Springer-Verlag (2009).Google Scholar

[14] I., Baković, B., Jurčo. The classifying topos of a topological bicategory. Homology, Homotopy Appl. 12 (2010), 279–300.

[15] C., Balteanu, Z., Fiedorowicz, R., Schwänzl, R., Vogt. Iterated monoidal categories. Adv. Math. 176 (2003), 277–349.Google Scholar

[16] C., Barwick. (∞, n) – Cat as a closed model category. Doctoral dissertation, University of Pennsylvania (2005).Google Scholar

[17] C., Barwick. ∞-groupoids, stacks, and Segal categories. Seminars 2004–2005 of the Mathematical Institute, University of Göttingen (Y. Tschinkel, ed.). Universitätsverlag Göttingen (2005), 155–195.

[18] C., Barwick. On (enriched) left Bousfield localization of model categories. Arxiv preprint arXiv:0708.2067 (2007), now in [20].

[19] C., Barwick. On Reedy model categories. Preprint arXiv: 0708.2832 (2007), now in [20].

[20] C., Barwick. On left and right model categories and left and right Bousfield localizations. Homology, Homotopy Appl. 1 (2010), 1–76.Google Scholar

[21] C., Barwick, D., Kan. Relative categories: Another model for the homotopy theory of homotopy theories. Preprint arXiv:1011.1691 (2010).

[22] C., Barwick, D., Kan. A Thomason-like Quillen equivalence between quasi-categories and relative categories. Preprint arXiv:1101.0772 (2011).

[23] C., Barwick, D., Kan. n-relative categories: a model for the homotopy theory of n-fold homotopy theories. Preprint arXiv:1102.0186 (2011).

[24] C., Barwick. On the Yoneda lemma and the strictification theorem for homotopy theories. Preprint (2008).

[25] M., Batanin. On the definition of weak ω-category. Macquarie mathematics report number 96/207, Macquarie University, Australia.

[26] M., Batanin. Monoidal globular categories as a natural environment for the theory of weak n-categories. Adv. Math. 136 (1998), 39–103.Google Scholar

[27] M., Batanin. Homotopy coherent category theory and A∞ structures in monoidal categories. J. Pure Appl. Alg. 123 (1998), 67–103.Google Scholar

[28] M., Batanin. On the Penon method of weakening algebraic structures. J. Pure Appl. Alg. 172 (2002), 1–23.Google Scholar

[29] M., Batanin. The Eckmann–Hilton argument and higher operads. Adv. Math. 217 (2008), 334–385.Google Scholar

[30] M., Batanin, D., Cisinski, M., Weber. Algebras of higher operads as enriched categories II. Preprint arXiv:0909.4715v1 (2009).

[31] F., Bauer, T., Datuashvili. Simplicial model category structures on the category of chain functors. Homology, Homotopy Appl. 9 (2007), 107–138.Google Scholar

[32] H., Baues. Combinatorial Homotopy and 4-Dimensional Complexes. de Gruyter, Berlin (1991).Google Scholar

[33] T., Beke. Sheafifiable homotopy model categories. Math. Proc. Cambridge Phil. Soc. 129 (2000), 447–475.Google Scholar

[34] J., Bénabou. Introduction to Bicategories. LECT. NOTES IN MATH. 47, Springer-Verlag (1967).Google Scholar

[35] C., Berger. Double loop spaces, braided monoidal categories and algebraic 3-type of space. Contemp. Math. 227 (1999), 49–65.Google Scholar

[36] C., Berger. A cellular nerve for higher categories. Adv. Math. 169 (2002), 118–175.Google Scholar

[37] C., Berger. Iterated wreath product of the simplex category and iterated loop spaces. Adv. Math. 213 (2007), 230–270.Google Scholar

[38] C., Berger, I., Moerdijk. On an extension of the notion of Reedy category. Math. Z. DOI 10.1007/s00209-010-0770-x (2010), 1–28.Google Scholar

[39] J., Bergner. A model category structure on the category of simplicial categories. Trans. Amer. Math. Soc. 359 (2007), 2043–2058.Google Scholar

[40] J., Bergner. Three models for the homotopy theory of homotopy theories. Topology 46 (2007), 397–436.Google Scholar

[41] J., Bergner. Adding inverses to diagrams encoding algebraic structures. Homology, Homotopy Appl. 10 (2008), 149–174.Google Scholar

[42] J., Bergner. A characterization of fibrant Segal categories. Proc. Amer. Math. Soc. 135 (2007), 4031–4037.Google Scholar

[43] J., Bergner. Rigidification of algebras over multi-sorted theories. Alg. Geom. Topol. 6 (2006), 1925–1955.Google Scholar

[44] J., Bergner. A survey of (∞, 1)-categories. In Towards Higher Categories (J., Baez, P., May, eds.). IMA VOLUMES MATH APPL. 152, Springer-Verlag (2009).Google Scholar

[45] J., Bergner. Simplicial monoids and Segal categories. Contemp. Math. 431 (2007), 59–83.Google Scholar

[46] J., Bergner. Homotopy fiber products of homotopy theories. Arxiv preprint arXiv:0811.3175 (2008).

[47] J., Bergner. Homotopy limits of model categories and more general homotopy theories. Arxiv preprint arXiv:1010.0717 (2010).

[48] J., Bergner. Models for (∞, n)-categories and the cobordism hypothesis. Arxiv preprint arXiv:1011.0110 (2010).

[49] B., Blander. Local projective model structures on simplicial presheaves. K-theory 24 (2001), 283–301.Google Scholar

[50] J., Boardman, R., Vogt. Homotopy Invariant Algebraic Structures on Topological Spaces. LECTURE NOTES IN MATH. 347, Springer-Verlag (1973).Google Scholar

[51] A., Bondal, M., Kapranov. Enhanced triangulated categories. Math. U.S.S.R. Sb. 70 (1991), 93–107.Google Scholar

[52] R., Bott, L., Tu. Differential Forms in Algebraic Topology. GRADUATE TEXTS IN MATH. 82, Springer-Verlag (1982).Google Scholar

[53] D., Bourn. Anadèses et catadèses naturelles. C.R. Acad. Sci. Paris Sér. A–B 276 (1973), A1401–A1404.Google Scholar

[54] D., Bourn. Sur les ditopos. C. R. Acad. Sci. Paris 279 (1974), 911–913.Google Scholar

[55] D., Bourn. La tour de fibrations exactes des n-catégories. Cah. Top. Géom. Différ. Catég. (1984).Google Scholar

[56] D., Bourn, J.-M., Cordier. A general formulation of homotopy limits. J. Pure Appl. Alg. 29 (1983), 129–141.Google Scholar

[57] A., Bousfield. Cosimplicial resolutions and homotopy spectral sequences in model categories. Geometry & Topology 7 (2003) 1001–1053.Google Scholar

[58] A., Bousfield, D., Kan. Homotopy Limits, Completions and Localizations. LECTURE NOTES IN MATH. 304, Springer-Verlag (1972).Google Scholar

[59] L., Breen. On the Classification of 2-Gerbs and 2-Stacks. ASTÉRISQUE 225, S.M.F. (1994).Google Scholar

[60] L., Breen. Monoidal categories and multiextensions. Compositio Math. 117 (1999), 295–335.Google Scholar

[61] E., Brown Jr, Finite computability of Postnikov complexes. Ann. Math. 65 (1957), 1–20Google Scholar

[62] K., Brown. Abstract homotopy theory and generalized sheaf cohomology. Trans. Amer. Math. Soc. 186 (1973), 419–458.Google Scholar

[63] K., Brown, S., Gersten. Algebraic K-theory as Generalized Sheaf Cohomology. LECTURE NOTES IN MATH. 341, Springer-Verlag (1973), 266–292.

[64] R., Brown. Groupoids and crossed objects in algebraic topology. Homology Homotopy Appl. 1 (1999), 1–78.Google Scholar

[65] R., Brown. Computing homotopy types using crossed n-cubes of groups. Adams Memorial Symposium on Algebraic Topology, Vol. 1 (N., Ray, G, Walker, eds.). Cambridge University Press (1992) 187–210.

[66] R., Brown, N.D., Gilbert. Algebraic models of 3-types and automorphism structures for crossed modules. Proc. London Math. Soc. (3) 59 (1989), 51–73.Google Scholar

[67] R., Brown, P., Higgins. The equivalence of ∞-groupoids and crossed complexes. Cah. Top. Géom. Différ. Catég. 22 (1981), 371–386.Google Scholar

[68] R., Brown, P., Higgins. The classifying space of a crossed complex. Math. Proc. Cambridge Phil. Soc. 110 (1991), 95–120.Google Scholar

[69] R., Brown, J.-L., Loday. Van Kampen theorems for diagrams of spaces. Topology 26 (1987), 311–335.Google Scholar

[70] R., Brown, J.-L., Loday. Homotopical excision, and Hurewicz theorems, for n-cubes of spaces. Proc. London Math. Soc. 54 (1987), 176–192.Google Scholar

[71] J., Cabello, A., Garzon. Closed model structures for algebraic models of n-types. J. Pure Appl. Alg. 103 (1995), 287–302.Google Scholar

[72] E., Cheng. The category of opetopes and the category of opetopic sets. Th. Appl. Cat. 11 (2003), 353–374.Google Scholar

[73] E., Cheng. An omega-category with all duals is an omega groupoid. Appl. Cat. Struct. 15 (2007), 439–453.Google Scholar

[74] E., Cheng. Comparing operadic theories of n-category. Preprint arXiv:0809.2070 (2008).

[75] E., Cheng, A., Lauda. Higher-Dimensional Categories: an Illustrated Guidebook (2004). http://cheng.staff.shef.ac.uk/guidebook/guidebook-new.pdfGoogle Scholar

[76] E., Cheng, M., Makkai. A note on the Penon definition of n-category. Preprint arXiv:0907.3961 (2009).

[77] D., Cisinski. Les Préfaisceaux Comme Modèles des Types d'Homotopie. ASTÉRISQUE 308, S.M.F. (2006).Google Scholar

[78] D., Cisinski. Batanin higher groupoids and homotopy types. In Categories in Algebra, Geometry and Mathematical Physics, Proceedings of Streetfest (M., Bataninet al., eds.), Contemporary Math. 431 (2007), 171–186.

[79] D., Cisinski. Propriétés universelles et extensions de Kan dérivées. Th. Appl. Cat. 20 (2008), 605–649.Google Scholar

[80] F., Cohen, T., Lada, J. P., May. The homology of iterated loop spaces. LECTURE NOTES IN MATH. 533, Springer-Verlag (1976).Google Scholar

[81] J., Cordier. Comparaison de deux catégories d'homotopie de morphismes cohérents. Cah. Top. Géom. Différ. Catég. 30 (1989), 257–275.Google Scholar

[82] J., Cordier, T., Porter. Vogt's theorem on categories of homotopy coherent diagrams. Math. Proc. Cambridge Phil. Soc. 100 (1986), 65–90.Google Scholar

[83] J., Cordier, T., Porter. Homotopy coherent category theory. Trans. Amer. Math. Soc. 349 (1997), 1–54.Google Scholar

[84] J., Cranch. Algebraic theories and (∞, 1)-categories. PhD thesis, University of Sheffield, arXiv:1011.3243 (2010).

[85] S., Crans. Quillen closed model structures for sheaves. J. Pure Appl. Alg. 101 (1995), 35–57.Google Scholar

[86] S., Crans. A tensor product for Gray-categories. Th. Appl. Cat. 5 (1999), 12–69.Google Scholar

[87] S., Crans. On braidings, syllapses and symmetries. Cah. Top. Géom. Différ. Catég. 41 (2000), 2–74.Google Scholar

[88] E., Curtis. Lower central series of semisimplicial complexes. Topology 2 (1963), 159–171.Google Scholar

[89] E., Curtis. Some relations between homotopy and homology. Ann. Math. 82 (1965), 386–413.Google Scholar

[90] P., Deligne. Théorie de Hodge, III. Publ. Math. I.H.E.S. 44 (1974), 5–77.Google Scholar

[91] P., Deligne, D., Mumford. On the irreducibility of the space of curves of a given genus. Publ. Math. I.H.E.S. 36 (1969), 75–109.Google Scholar

[92] P., Deligne, A., Ogus, J., Milne, K., Shih. Hodge Cycles, Motives, and Shimura Varieties. LECTURE NOTES IN MATH. 900, Springer-Verlag (1982).Google Scholar

[93] V., Drinfeld. DG quotients of DG categories. J. Alg. 272 (2004), 643–691.Google Scholar

[94] E., Dror Farjoun, A., Zabrodsky. The homotopy spectral sequence for equivariant function complexes. In Algebraic Topology, Barcelona, 1986. LECTURE NOTES IN MATH. 1298, Springer-Verlag (1987), 54–81.Google Scholar

[95] D., Dugger. Combinatorial model categories have presentations. Adv. Math. 164 (2001), 177–201.Google Scholar

[96] D., Dugger, D., Spivak. Mapping spaces in quasi-categories. Preprint arXiv:0911. 0469 (2009).

[97] G., Dunn. Uniqueness of n-fold delooping machines. J. Pure Appl. Alg. 113 (1996), 159–193.Google Scholar

[98] J., Duskin. Simplicial matrices and the nerves of weak n-categories I: nerves of bicategories. Th. Appl. Cat. 9 (2002), 198–308.Google Scholar

[99] W., Dwyer, P., Hirschhorn, D., Kan. Model categories and more general abstract homotopy theory, a work in what we like to think of as progress. (This historically important manuscript was later integrated into the next reference.)

[100] W., Dwyer, P., Hirschhorn, D., Kan, J., Smith. Homotopy Limit Functors on Model Categories and Homotopical Categories. MATH. SURVEYS AND MONOGRAPHS 113, A.M.S. (2004).Google Scholar

[101] W., Dwyer, D., Kan. Simplicial localizations of categories. J. Pure Appl. Alg. 17 (1980), 267–284.Google Scholar

[102] W., Dwyer, D., Kan. Calculating simplicial localizations. J. Pure Appl. Alg. 18 (1980), 17–35.Google Scholar

[103] W., Dwyer, D., Kan. Function complexes in homotopical algebra. Topology 19 (1980), 427–440.Google Scholar

[104] W., Dwyer, D., Kan, J., Smith. Homotopy commutative diagrams and their realizations. J. Pure Appl. Alg. 57 (1989), 5–24.Google Scholar

[105] W., Dwyer, J., Spalinski. Homotopy theories and model categories. In Handbook of Algebraic Topology (I. M., James, ed.), Elsevier (1995).Google Scholar

[106] J., Dydak. A simple proof that pointed, connected FANR spaces are regular fundamental retracts of ANRs. Bull. Acad. Polon. Sci. Ser. Sci. Math. Phys. 25 (1977), 55–62.Google Scholar

[107] J., Dydak. 1-movable continua need not be pointed 1-movable. Bull. Acad. Polon. Sci. Ser. Sci. Math. Phys. 25 (1977), 485–488.Google Scholar

[108] E., Dyer, R., Lashoff. Homology of iterated loop spaces. Amer. J. Math. 84 (1962), 35–88.Google Scholar

[109] J., Elgueta. On the regular representation of an (essentially) finite 2-group. Preprint arXiv:0907.0978 (2009).

[110] G., Ellis. Spaces with finitely many nontrivial homotopy groups all of which are finite. Topology 36 (1997), 501–504.Google Scholar

[111] Z., Fiedorowicz. Classifying spaces of topological monoids and categories. Amer. J. Math. 106 (1984), 301–350.Google Scholar

[112] Z., Fiedorowicz, R., Vogt. Simplicial n-fold monoidal categories model all n-fold loop spaces. Cah. Top. Géom. Différ. Catég. 44 (2003), 105–148.Google Scholar

[113] T., Fiore. Pseudo limits, biadjoints, and pseudo algebras: categorical foundations of conformal field theory. Mem. Amer. Math. Soc. 182 (2006).Google Scholar

[114] P., Freyd, A., Heller. Splitting homotopy idempotents, II. J. Pure Appl. Alg. 89 (1993), 93–106.Google Scholar

[115] K., Fukaya. Morse homotopy, A∞-category and Floer homologies. In Proceedings of GARC Workshop on Geometry and Topology (H. J., Kim, ed.), Seoul National University, (1993).Google Scholar

[116] C., Futia. Weak omega categories I. Preprint arXiv:math/0404216 (2004).

[117] P., Gabriel, M., Zisman. Calculus of Fractions and Homotopy Theory. Springer-Verlag (1967).Google Scholar

[118] N., Gambino. Homotopy limits for 2-categories. Math. Proc. Cambridge Phil. Soc. 145 (2008), 43–63.Google Scholar

[119] R., Garner, N., Gurski. The low-dimensional structures that tricategories form. Preprint arXiv:0711.1761 (2007).

[120] P., Gaucher. Homotopy invariants of higher dimensional categories and concurrency in computer science. Math. Struct. Comp. Sci. 10 (2000), 481–524.Google Scholar

[121] J., Giraud. Cohomologie Nonabélienne. GRUNDLEHREN DER WISSENSCHAFTEN IN EINZELDARSTELLUNG 179, Springer-Verlag (1971).Google Scholar

[122] P., Goerss, R., Jardine. Simplicial Homotopy Theory. PROGRESS IN MATH. 174, Birkhäuser (1999).Google Scholar

[123] R., Gordon, A.J., Power, R., Street. Coherence for tricategories. Memoirs A.M.S. 117 (1995), 558 ff.Google Scholar

[124] M., Grandis. Directed homotopy theory, I. The fundamental category. Cah. Top. Géom. Différ. Catég. 44 (2003), 281–316.Google Scholar

[125] M., Grandis, R., Paré. Limits in double categories. Cah. Top. Géom. Différ. Catég. 40 (1999), 162–220.Google Scholar

[126] J., Gray. Formal Category Theory: Adjointness for 2-Categories. LECTURE NOTES IN MATH. 391, Springer-Verlag (1974).Google Scholar

[127] J., Gray. Closed categories, lax limits and homotopy limits. J. Pure Appl. Alg. 19 (1980), 127–158.Google Scholar

[128] J., Gray. The existence and construction of lax limits. Cah. Top. Géom. Différ. Catég. 21 (1980), 277–304.Google Scholar

[129] A., Grothendieck. Sur quelques points d'algèbre homologique, I. Tohoku Math. J. 9 (1957), 119–221.Google Scholar

[130] A., Grothendieck. Techniques de construction et théorèmes d'existence en géométrie algébrique. III. Préschemas quotients. Séminaire Bourbaki, 13e année, 1960/61 212 (1961).Google Scholar

[131] A., Grothendieck. Revetements Etales et Groupe Fondamental (SGA I), LECTURE NOTES IN MATH. 224, Springer-Verlag (1971).Google Scholar

[132] A., Grothendieck. Pursuing Stacks.

[133] A., Grothendieck. Les Dérivateurs (G., Maltsiniotis, ed.) Available online at http://people.math.jussieu.fr/ maltsin/textes.html.

[134] N., Gurski. An algebraic theory of tricategories. Ph.D. thesis, University of Chicago (2006).

[135] R., Hain. Completions of mapping class groups and the cycle C – C-. In Mapping Class Groups and Moduli Spaces of Riemann Surfaces: Proceedings of Workshops held in Göttingen and Seattle. CONTEMPORARY MATH. 150, A.M.S. (1993), 75–106.Google Scholar

[136] R., Hain. The de rham homotopy theory of complex algebraic varieties I. K-theory 1 (1987), 271–324.Google Scholar

[137] R., Hain. The Hodge de Rham theory of relative Malcev completion. Ann. Sci. de l'E.N.S. 31 (1998), 47–92.Google Scholar

[138] H., Hastings, A., Heller. Splitting homotopy idempotents. In Shape Theory and Geometric Topology (Dubrovnik, 1981). LECTURE NOTES IN MATH. 870, Springer-Verlag (1981), 23–36.Google Scholar

[139] H., Hastings, A., Heller. Homotopy idempotents on finite-dimensional complexes split. Proc. Amer. Math. Soc. 85 (1982), 619–622.Google Scholar

[140] A., Heller. Homotopy in functor categories. Trans. Amer. Math. Soc. 272 (1982), 185–202.Google Scholar

[141] A., Heller. Homotopy theories. Mem. Amer. Math. Soc. 71 (388) (1988).Google Scholar

[142] C., Hermida, M., Makkai, A., Power. On weak higher-dimensional categories I. J. Pure Appl. Alg. Part 1: 154 (2000), 221–246; Part 2: 157 (2001), 247–277; Part 3: 166 (2002), 83–104.Google Scholar

[143] V., Hinich. Homological algebra of homotopy algebras. Comm. Alg. 25 (1997), 3291–3323.Google Scholar

[144] P., Hirschhorn. Model Categories and their Localizations. MATH. SURVEYS AND MONOGRAPHS 99, A.M.S. (2003).

[145] A., Hirschowitz, C., Simpson. Descente pour les n-champs. Preprint math/9807049 (1998).

[146] J., Hirsh, J., Millès. Curved Koszul duality theory. Preprint, University of Nice (2010).

[147] S., Hollander. A homotopy theory for stacks. Israel J. Math. 163 (2008) 93–124.Google Scholar

[148] M., Hovey. Monoidal model categories. Arxiv preprint math/9803002 (1998).

[149] M., Hovey. Model Categories. MATH. SURVEYS AND MONOGRAPHS 63, A.M.S. (1999).

[150] L., Illusie. Complexe Cotangent et Déformations, II. LECTURE NOTES IN MATH. 283, Springer-Verlag (1972).Google Scholar

[151] I., James. Reduced product spaces. Ann. Math. 62 (1955), 170–197.Google Scholar

[152] G., Janelidze. Precategories and Galois theory. Springer-Verlag (1990).Google Scholar

[153] J.F., Jardine. Simplicial presheaves, J. Pure Appl. Alg. 47 (1987), 35–87.Google Scholar

[154] M., Johnson. The combinatorics of n-categorical pasting. J. Pure Appl. Alg. 62 (1989), 211–225.Google Scholar

[155] M., Johnson. On modified Reedy and modified projective model structures. Preprint arXiv:1004.3922v1 (2010).

[156] A., Joyal. Letter to A. Grothendieck (referred to in Jardine's paper).

[157] A., Joyal. Quasi-categories and Kan complexes. J. Pure Appl. Alg. 175 (2002), 207–222.Google Scholar

[158] A., Joyal. Disks, duality and θ-categories. Preprint (1997).

[159] A., Joyal, J., Kock. Weak units and homotopy 3-types. In Categories in Algebra, Geometry and Mathematical Physics: Conference and Workshop in Honor of Ross Street's 60th Birthday. CONTEMPORARY MATH. 431, A.M.S (2007), 257–276.Google Scholar

[160] A., Joyal, J., Kock. Coherence for weak units. Preprint arXiv:0907.4553 (2009).

[161] A., Joyal, M., Tierney. Algebraic homotopy types. Occurs as an entry in the bibliography of [8].

[162] A., Joyal, M., Tierney. Quasi-categories vs Segal spaces. In Categories in Algebra, Geometry and Mathematical Physics: Conference and Workshop in Honor of Ross Street's 60th Birthday. CONTEMPORARY MATH. 431, A.M.S. (2007), 277–326.Google Scholar

[163] D., Kan. On c.s.s. complexes. Amer. J. Math. 79 (1957), 449–476.Google Scholar

[164] D., Kan. A combinatorial definition of homotopy groups. Ann. Math. 67 (1958), 282–312.Google Scholar

[165] D., Kan. On homotopy theory and c.s.s. groups. Ann. Math. 68 (1958), 38–53.Google Scholar

[166] D., Kan. On c.s.s. categories. Bol. Soc. Math. Mexicana (1957), 82–94.Google Scholar

[167] M., Kapranov. On the derived categories of coherent sheaves on some homogeneous spaces. Invent. Math. 92 (1988), 479–508.Google Scholar

[168] M., Kapranov, V., Voevodsky. ∞-groupoids and homotopy types. Cah. Top. Géom. Différ. Catég. 32 (1991), 29–46.Google Scholar

[169] L., Katzarkov, T., Pantev, B., Toën. Algebraic and topological aspects of the schematization functor. Compositio Math. 145 (2009), 633–686.Google Scholar

[170] B., Keller. Deriving DG categories. Ann. Sci. E.N.S. 27 (1994), 63–102.Google Scholar

[171] G., Kelly, Basic concepts of enriched category theory. LONDON MATH. SOC. LECTURE NOTES 64, Cambridge University Press (1982).Google Scholar

[172] J., Kock. Weak identity arrows in higher categories. Int. Math. Res. Papers (2006).Google Scholar

[173] J., Kock. Elementary remarks on units in monoidal categories. Math. Proc. Cambridge Phil. Soc. 144 (2008), 53–76.Google Scholar

[174] J., Kock, A., Joyal, M., Batanin, J., Mascari. Polynomial functors and opetopes. Adv. Math. 224 (2010), 2690–2737.Google Scholar

[175] G., Kondratiev. Concrete duality for strict infinity categories. Preprint arXiv:0807.4256 (2008) (see also arXiv:math/0608436).

[176] M., Kontsevich. Homological algebra of mirror symmetry. In Proceedings of I.C.M.-94, Zurich. Birkhäuser (1995), 120–139.Google Scholar

[177] J.-L., Krivine. Théorie Axiomatique des Ensembles, Presses Universitaires de France (1969); English translation by D. Miller, Introduction to Axiomatic Set Theory, D. Reidel Publishing Co. (1971).Google Scholar

[178] S., Lack. A Quillen model structure for Gray-categories. Preprint arXiv:1001. 2366 (2010).

[179] Y., Lafont, F., Métayer, K., Worytkiewicz. A folk model structure on omega-cat. Adv. Math. 224 (2010), 1183–1231.Google Scholar

[180] G., Laumon, L., Moret-Bailly. Champs Algébriques. Springer-Verlag (2000).Google Scholar

[181] F. W., Lawvere. Functorial semantics of algebraic theories. Proc. Nat. Acad. Sci. 50 (1963), 869–872.Google Scholar

[182] F. W., Lawvere. Functorial semantics of algebraic theories, Dissertation, Columbia University 1963; reprint in Th. Appl. Cat.5 (2004), 23–107.

[183] T., Leinster. A survey of definitions of n-category. Th. Appl. Cat. 10 (2002,E;), 1–70.Google Scholar

[184] T., Leinster. Higher Operads, Higher Categories. LONDON MATH. SOC. LECTURE NOTES 298, Cambridge University Press (2004).

[185] T., Leinster. Up-to-homotopy monoids. Arxiv preprint math/9912084 (1999).

[186] O., Leroy. Sur une notion de 3-catégorie adaptée à l'homotopie. Preprint Univ. de Montpellier 2 (1994).

[187] L. G., Lewis. Is there a convenient category of spectra?J. Pure Appl. Alg. 73 (1991), 233–246.Google Scholar

[188] J.-L., Loday. Spaces with finitely many non-trivial homotopy groups. J. Pure Appl. Alg. 24 (1982), 179–202.Google Scholar

[189] J., Lurie. On infinity topoi. Preprint arXiv:math/0306109 (2003).

[190] J., Lurie. Higher topos theory. Ann. Math. Studies 170 (2009).Google Scholar

[191] J., Lurie. Derived Algebraic Geometry II–VI. Arxiv preprints (2007–2009).

[192] J., Lurie. (Infinity,2)-Categories and the Goodwillie Calculus I. Preprint arXiv:0905.0462v2 (2009).

[193] J., Lurie. On the classification of topological field theories. Current Developments in Mathematics Vol. 2008 (2009), 129–280.Google Scholar

[194] D., McDuff. On the classifying spaces of discrete monoids. Topology 18 (1979), 313–320.Google Scholar

[195] M., Mackaay. Spherical 2-categories and 4-manifold invariants. Adv. Math. 143 (1999), 288–348.Google Scholar

[196] S., Mac Lane. Categories for the Working Mathematician. GRADUATE TEXTS IN MATH. 5, Springer-Verlag (1971).

[197] M., Makkai, R., Paré. Accessible Categories: The Foundations of Categorical Model Theory. CONTEMPORARY MATH. 104, A.M.S. (1989).

[198] G., Maltsiniotis. La Théorie de l'Homotopie de Grothendieck. ASTÉRISQUE 301, S.M.F. (2005).

[199] G., Maltsiniotis. Infini groupoïdes non stricts, d'après Grothendieck. Preprint (2007).

[200] G., Maltsiniotis. Infini catégories non strictes, une nouvelle définition. Preprint (2007).

[201] W., Massey. Algebraic Topology: An Introduction. GRADUATE TEXTS IN MATH. 56, Springer-Verlag (1977).

[202] J. P., May. Simplicial Objects in Algebraic Topology. Van Nostrand (1967).Google Scholar

[203] J.P., May. The Geometry of Iterated Loop Spaces. LECTURE NOTES IN MATH. 271, Springer-Verlag (1972).Google Scholar

[204] J. P., May. Classifying spaces and fibrations. Mem. Amer. Math. Soc. 155 (1975).Google Scholar

[205] J. P., May, R., Thomason. The uniqueness of infinite loop space machines. Topology 17 (1978), 205–224.Google Scholar

[206] S., Mochizuki. Idempotent completeness of higher derived categories of abelian categories. K-theory preprint archives n. 970 (2010).

[207] F., Morel, V., Voevodsky. A1-homotopy theory of schemes. Publ. Math. I.H.E.S. 90 (1999), 45–143.Google Scholar

[208] S., Moriya. Rational homotopy theory and differential graded category. J. Pure Appl. Alg. 214 (2010), 422–439.Google Scholar

[209] J., Nichols-Barrer. On quasi-categories as a foundation for higher algebraic stacks. Ph.D. thesis, M.I.T. (2007).

[210] S., Paoli. Weakly globular catn-groups and Tamsamani's model. Adv. Math. 222 (2009), 621–727.Google Scholar

[211] R., Pellissier. Catégories enrichies faibles. Thesis, Université de Nice (2002), available online at http://tel.archives-ouvertes.fr/tel-00003273/fr/.

[212] J., Penon. Approche polygraphique des ∞-catégories non strictes. Cah. Top. Géom. Différ. Catég. 40 (1999), 31–80.Google Scholar

[213] A., Power. Why tricategories? Information and Computation 120 (1995), 251–262.Google Scholar

[214] J., Pridham. Pro-algebraic homotopy types. Proc. London Math. Soc. 97 (2008), 273–338.Google Scholar

[215] D., Quillen. Homotopical Algebra. LECTURE NOTES IN MATH. 43, Springer-Verlag (1967).Google Scholar

[216] D., Quillen. Rational homotopy theory. Ann. Math. 90 (1969), 205–295.Google Scholar

[217] C., Reedy. Homotopy theory of model categories. Preprint (1973) available from P. Hirschhorn.

[218] C., Rezk. A model for the homotopy theory of homotopy theory. Trans. Amer. Math. Soc. 353 (2001), 973–1007.Google Scholar

[219] C., Rezk. A cartesian presentation of weak n-categories. Geometry & Topology 14 (2010), 521–571.Google Scholar

[220] E., Riehl. On the structure of simplicial categories associated to quasi-categories. Preprint arXiv:0912.4809 (2009).

[221] J., Rosický and W., Tholen, Left-determined model categories and universal homotopy theories. Trans. Amer. Math. Soc. 355 (2003), 3611–3623.Google Scholar

[222] J., Rosický. On homotopy varieties. Adv. Math. 214 (2007), 525–550.Google Scholar

[223] J., Rosický. On combinatorial model categories. Appl. Cat. Structures 17 (2009) 303–316.Google Scholar

[224] R., Schwänzl, R., Vogt. Homotopy homomorphisms and the hammock localization. Papers in Honor of José Adem, Bol. Soc. Mat. Mexicana 37 (1992), 431–448.Google Scholar

[225] G., Segal. Homotopy everything H-spaces. Preprint.

[226] G., Segal. Classifying spaces and spectral sequences. Publ. Math. IHES 34 (1968), 105–112.Google Scholar

[227] G., Segal. Configuration spaces and iterated loop spaces. Invent. Math. 21 (1973), 213–221.Google Scholar

[228] G., Segal. Categories and cohomology theories. Topology 13 (1974), 293–312.Google Scholar

[229] B., Shipley, S., Schwede. Equivalences of monoidal model categories. Algebr. Geom. Topol. 3 (2003), 287–334.Google Scholar

[230] C., Simpson. Homotopy over the complex numbers and generalized de Rham cohomology. In Moduli of Vector Bundles (M., Maruyama, ed.). LECTURE NOTES IN PURE AND APPLIED MATH. 179, Marcel Dekker (1996), 229–263.Google Scholar

[231] C., Simpson. Flexible sheaves. Preprint q-alg/9608025 (1996).

[232] C., Simpson. The topological realization of a simplicial presheaf. Preprint q-alg/9609004 (1996).

[233] C., Simpson. Algebraic (geometric) n-stacks. Preprint alg-geom/9609014 (1996).

[234] C., Simpson. A closed model structure for n-categories, internal Hom, n-stacks and generalized Seifert-Van Kampen. Preprint alg-geom/9704006 (1997).

[235] C., Simpson. Limits in n-categories. Preprint alg-geom 9708010 (1997).

[236] C., Simpson. Effective generalized Seifert–Van Kampen: how to calculate ΩX. Preprint q-alg/9710011 (1997).

[237] C., Simpson. On the Breen–Baez–Dolan stabilization hypothesis. Preprint math.CT/9810058 (1998).

[238] C., Simpson. Homotopy types of strict 3-groupoids. Preprint, math.CT/9810059 (1998).

[239] J., Smith. Combinatorial model categories. Unpublished manuscript referred to in [95].

[240] A., Stanculescu. A homotopy theory for enrichment in simplicial modules. Preprint arXiv:0712.1319 (2007).

[241] J., Stasheff. Homotopy associativity of H-spaces, I, II. Trans. Amer. Math. Soc. 108 (1963), 275–292, 293–312.Google Scholar

[242] R., Street. Elementary cosmoi, I. In Category Seminar (Sydney, 1972/1973). LECTURE NOTES IN MATH. 420, Springer-Verlag (1974), 134–180.Google Scholar

[243] R., Street. Limits indexed by category-valued 2-functors. J. Pure Appl. Alg. 8 (1976), 149–181.Google Scholar

[244] R., Street. The algebra of oriented simplexes. J. Pure Appl. Alg. 49 (1987), 283–335.Google Scholar

[245] R., Street. Weak ω-categories. Diagrammatic Morphisms and Applications (San Francisco, 2000) Contemporary Mathematics 318, A.M.S. (2003), 207–213.Google Scholar

[246] G., Tabuada. Differential graded versus Simplicial categories. Top. Appl. 157 (2010), 563–593.Google Scholar

[247] G., Tabuada. Homotopy theory of spectral categories. Adv. Math. 221 (2009), 1122–1143.Google Scholar

[248] Z., Tamsamani. Sur des notions de n-catégorie et n-groupoïde non-stricte via des ensembles multi-simpliciaux. Thesis, Université Paul Sabatier, Toulouse (1996), first part available as alg-geom/9512006.

[249] Z., Tamsamani. Equivalence de la théorie homotopique des n-groupoïdes et celle des espaces topologiques n-tronqués. Preprint alg-geom alg-geom/9607010 (1996).

[250] Z., Tamsamani. Sur des notions de n-catégorie et n-groupoïde non-stricte via des ensembles multi-simpliciaux. K-theory 16 (1999), 51–99.Google Scholar

[251] D., Tanre. Homotopie Rationnelle: Modèles de Chen, Quillen, Sullivan. LECTURE NOTES IN MATH. 1025, Springer-Verlag (1983).

[252] R., Thomason. Homotopy colimits in the category of small categories. Math. Proc. Cambridge Phil. Soc. 85 (1979), 91–109.Google Scholar

[253] R., Thomason. Uniqueness of delooping machines. Duke Math. J. 46 (1979), 217–252.Google Scholar

[254] R., Thomason. Algebraic K-theory and étale cohomology. Ann. Sci. E.N.S. 18 (1985), 437–552.Google Scholar

[255] B., Toën. Champs affines. Selecta Math. 12 (2006), 39–134.Google Scholar

[256] B., Toën. Vers une axiomatisation de la théorie des catégories supérieures. K-theory 34 (2005), 233–263.Google Scholar

[257] B., Toën. The homotopy theory of dg-categories and derived Morita theory. Invent. Math. 167 (2007), 615–667.Google Scholar

[258] B., Toën. Anneaux de définition des dg-algèbres propres et lisses. Bull. Lond. Math. Soc. 40 (2008), 642–650.Google Scholar

[259] T., Trimble. Notes on tetracategories. Available online at http://math.ucr.edu/home/baez/trimble/tetracategories.html.

[260] D., Verity. Weak complicial sets I. Basic homotopy theory. Adv. Math. 219 (2008), 1081–1149.Google Scholar

[261] V., Voevodsky. The Milnor conjecture. Preprint (1996).

[262] R., Vogt. Homotopy limits and colimits. Math. Z. 134 (1973), 11–52.Google Scholar

[263] R., Vogt. The HELP-Lemma and its converse in Quillen model categories. Preprint arXiv:1004.5249v1 (2010).

[264] M., Weber. Yoneda Structures from 2-toposes. Appl. Cat. Struct. 15 (2007), 259–323.Google Scholar

[265] G., Whitehead. Elements of Homotopy Theory. Springer-Verlag (1978).Google Scholar

[266] J. H. C., Whitehead. On the asphericity of regions in a 3-sphere. Fund. Math. 32 (1939), 149–166.Google Scholar

[267] M., Zawadowski. Lax Monoidal Fibrations. Preprint arXiv:0912.4464 (2009).