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References

Published online by Cambridge University Press:  01 June 2011

J. Adámek
Affiliation:
Technische Universität Carolo Wilhelmina zu Braunschweig, Germany
J. Rosický
Affiliation:
Masarykova Univerzita v Brně, Czech Republic
E. M. Vitale
Affiliation:
Université Catholique de Louvain, Belgium
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Algebraic Theories
A Categorical Introduction to General Algebra
, pp. 241 - 244
Publisher: Cambridge University Press
Print publication year: 2010

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References

Adámek, J. (1974). Free algebras and automata realizations in the language of categories. Comment. Math. Univ. Carolina. 14: 589–602.Google Scholar
Adámek, J. (1977). Colimits of algebras revisited. Bull. Austral. Math. Soc. 17: 433–450.CrossRefGoogle Scholar
Adámek, J., F., Borceux, S., Lack, and J., Rosický (2002). A classification of accessible categories. J. Pure Appl. Algebra 175: 7–30.CrossRefGoogle Scholar
Adámek, J., H., Herrlich, and G., Strecker (2009). Abstract and Concrete Categories. Dover.Google Scholar
Adámek, J., F. W., Lawvere, and J., Rosický (2001a). How algebraic is algebra? Theory Appl. Categ. 8: 253–283.Google Scholar
Adámek, J., F. W., Lawvere, and J., Rosický (2003). On the duality between varieties and algebraic theories. Alg. Univ. 49: 35–49.CrossRefGoogle Scholar
Adámek, J., and H.-E., Porst (1998). Algebraic theories of quasivarieties. J. Algebra 208: 379–398.CrossRefGoogle Scholar
Adámek, J., and J., Rosický (1994). Locally Presentable and Accessible Categories. Cambridge University Press.CrossRefGoogle Scholar
Adámek, J., and J., Rosický (2001). On sifted colimits and generalized varieties. Theory Appl. Categ. 8: 33–53.Google Scholar
Adámek, J., J., Rosický, and E. M., Vitale (2001b). On algebraically exact categories and essential localizations of varieties. J. Algebra 244: 450–477.CrossRefGoogle Scholar
Adámek, J., J., Rosický, and E. M., Vitale (2010). What are sifted colimits? Theory Appl. Categ. 23: 251–260Google Scholar
Adámek, J., M., Sobral, and L., Sousa (2006). Morita equivalence for many-sorted algebraic theories. J. Algebra 297: 361–371.CrossRefGoogle Scholar
Almeida, J. (1994). Finite Semigroups and Universal Algebra. World Scientific.Google Scholar
Artin, M., A., Grothendieck, and J. L., Verdier (1972). Théorie des topos et cohomologie étale des schémas. Lect. Notes in Math. 269. Springer.Google Scholar
Banaschewski, B. (1972). Functors into categories of M-sets. Abh. Mat. Sem. Univ. Hamburg 38: 49–64.CrossRefGoogle Scholar
Barr, M. (1970). Coequalizers and free triples. Math. Z. 116: 307–322.CrossRefGoogle Scholar
Barr, M., A. P., Grillet, and D. H., van Osdol (1971). Exact Categories and Categories of Sheaves. Lect. Notes in Math. 236. Springer.CrossRefGoogle Scholar
Barr, M., and C., Wells (1985). Toposes, Triples and Theories. Springer.CrossRefGoogle Scholar
Barr, M., and C., Wells (1990). Category Theory for Computing Science. Prentice Hall.Google Scholar
Bass, H. (1968). Algebraic K-Theory. Benjamin.Google Scholar
Bastiani, A., and C., Ehresmann (1972). Categories of sketched structures. Cah. Top. Géom. Différ. Catég. 13: 104–214.Google Scholar
Bénabou, J. (1967). Introduction to bicategories. In Reports of the Midwest Category Seminar. Lect. Notes in Math. 40. Springer, 1–77.CrossRefGoogle Scholar
Bénabou, J. (1968). Structures algébriques dans les catégories. Cah. Top. Géom. Différ. Catég. 10: 1–126.Google Scholar
Birkhoff, G. (1935). On the structure of abstract algebras. Proc. Cambr. Phil. Soc. 31: 433–454.CrossRefGoogle Scholar
Birkhoff, G., and J. D., Lipson (1970). Heterogenous algebras. J. Combin. Theory 8: 115–133.CrossRefGoogle Scholar
Boardman, J. M., and R. M., Vogt (1973). Homotopy Invariant Algebraic Structures on Topological Spaces. Lect. Notes in Math. 347. Springer.CrossRefGoogle Scholar
Borceux, F. (1994). Handbook of Categorical Algebra. Cambridge University Press.Google Scholar
Borceux, F., and E. M., Vitale (1994). On the notion of bimodel for functorial semantics. Appl. Categ. Struct. 2: 283–295.CrossRefGoogle Scholar
Bourbaki, N. (1956). Théorie des Ensembles. Herrman.Google Scholar
Bunge, M. (1966). Categories of set-valued functors. Dissertation, University of Pennsylvania.
Bunge, M., and A., Carboni (1995). The symmetric topos. J. Pure Appl. Algebra 105: 233–249.CrossRefGoogle Scholar
Carboni, A., and R., Celia Magno (1982). The free exact category on a left exact one. J. Austral. Math. Soc. Ser. A 33: 295–301.CrossRefGoogle Scholar
Carboni, A., and E. M., Vitale (1998). Regular and exact completions. J. Pure Appl. Algebra 125: 79–116.CrossRefGoogle Scholar
Centazzo, C., J., Rosický, and E. M., Vitale (2004). A characterization of locally D-presentable categories. Cah. Top. Géom. Différ. Catég. 45: 141–146.Google Scholar
Centazzo, C., and E. M., Vitale (2002). A duality relative to a limit doctrine. Theory Appl. Categ. 10: 486–497.Google Scholar
Cohn, P. M. (1965). Universal Algebra. Harper and Row.Google Scholar
Diers, Y. (1976). Type de densité d'une sous-catégorie pleine. Ann. Soc. Sc. Bruxelles 90: 25–47.Google Scholar
Dukarm, J. J. (1988). Morita equivalence of algebraic theories. Colloq. Math. 55: 11–17.CrossRefGoogle Scholar
Ehresmann, C. (1963). Catégories structurées. Ann. Sci. École Norm. Sup. 80: 349–426.CrossRefGoogle Scholar
Ehresmann, C. (1967). Sur les structures algébriques. C. R. Acad. Sci. Paris 264: A840–A843.Google Scholar
Eilenberg, S. (1961). Abstract description of some basic functors. J. Indian Math. Soc. (N. S.) 24: 231–234.Google Scholar
Elkins, B., and J. A., Zilber (1976). Categories of actions and Morita equivalence. Rocky Mountain J. Math. 6: 199–225.CrossRefGoogle Scholar
Gabriel, P. (1962). Des catégories abéliennes. Bull. Sci. Math. France 90: 323–448.CrossRefGoogle Scholar
Gabriel, P., and F., Ulmer (1971). Lokal Präsentierbare Kategorien. Lect. Notes in Math. 221. Springer.CrossRefGoogle Scholar
Gran, M., and E. M., Vitale (1998). On the exact completion of the homotopy category. Cahiers Top. Géom. Diff. Cat. 39: 287–297.Google Scholar
Grätzer, G. (2008). Universal Algebra. Springer.CrossRefGoogle Scholar
Hagemann, J., and C., Hermann (1979). A concrete ideal multiplication for algebraic systems and its relation to congruence modularity. Arch. Math. (Basel) 32: 234–245.CrossRefGoogle Scholar
Heller, A. (1965). MR0163940. Math. Rev. 29.Google Scholar
Higgins, P. J. (1963–1964). Algebras with a scheme of operators. Math. Nachr. 27: 115–132.CrossRefGoogle Scholar
Hyland, M., and J., Power (2007). The category theoretic understanding of universal algebra: Lawvere theories and monads. Electron. Notes Theor. Comput. Sci. 172: 437–458.CrossRefGoogle Scholar
Janelidze, Z. (2006). Closedness properties of internal relations I: A unified approach to Mal'tsev, unital and subtractive categories. Theory Appl. Categ. 16: 236–261.Google Scholar
Janelidze, G., and M. C., Pedicchio (2001). Pseudogroupoids and commutators. Theory Appl. Categ. 8: 408–456.Google Scholar
Joyal, A. (2008). Notes on logoi (unpublished book in preparation).
Kelly, G. M. (1982). Basic Concepts of Enriched Categories. Cambridge University Press.Google Scholar
Lack, S., and J., Rosický (2010). Notions of Lawvere theory. Appl. Cat. Struct. (In press).Google Scholar
Lair, C. (1996). Sur le genre d'esquissabilité des catégories modelables (accessibles) possédant les produits de deux. Diagrammes 35: 25–52.Google Scholar
Lambek, J. (1968). A fixpoint theorem for complete categories. Math. Z. 103: 151–161.CrossRefGoogle Scholar
Lawvere, F. W. (1963). Functorial semantics of algebraic theories. Dissertation, Columbia University.
Lawvere, F. W. (1969). Ordinal sums and equational doctrines. In Seminar on Triples and Categorical Homology Theory. Lect. Notes in Math. 80: Springer, 141–155.CrossRefGoogle Scholar
Lawvere, F. W. (2008). Core varieties, extensivity, and rig geometry. Theory Appl. Categ. 20: 497–503.Google Scholar
Linton, F. E. J. (1966). Some aspects of equational categories. In Proc. Conf. Categorical Algebra La Jolla 1965. Springer, 84–94.Google Scholar
Linton, F. E. J. (1969a). Coequalizers in categories of algebras. In Seminar on Triples and Categorical Homology Theory. Lect. Notes in Math. 80. Springer, 75–90.CrossRefGoogle Scholar
Linton, F. E. J. (1969b). Applied functorial semantics, II. In Seminar on Triples and Categorical Homology Theory. Lect. Notes in Math. 80. Springer, 53–74.CrossRefGoogle Scholar
Loday, J.-L. (2008). Generalized Bialgebras and Triples of Operads. Astérisque.Google Scholar
Lurie, J. (2009). Higher Topos Theory. Princeton University Press.Google Scholar
Mac Lane, S. (1963). Natural associativity and commutativity. Rice Univ. Stud. 49: 38–46.Google Scholar
Mac Lane, S. (1998). Categories for the Working Mathematician. Springer.Google Scholar
Makkai, M., and R., Paré (1989). Accessible Categories: The Foundation of Categorical Model Theory. Contemp. Math. 104. AMS.CrossRefGoogle Scholar
Manes, E. G. (1976). Algebraic Theories. Springer.CrossRefGoogle Scholar
McKenzie, R. N. (1996). An algebraic version of categorical equivalence for varieties and more general categories. Lect. Notes Pure Appl. Mathematics 180. Marcel Dekker, 211–243.Google Scholar
Mitchell, B. (1965). Theory of Categories. Academic.Google Scholar
Morita, K. (1958). Duality for modules and its applications to the theory of rings with minimum conditions. Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A 6: 83–142.Google Scholar
Pareigis, B. (1970). Categories and Functors. Academic.Google Scholar
Pedicchio, M. C. (1995). A categorical approach to commutator theory. J. Algebra 177: 647–657.CrossRefGoogle Scholar
Pedicchio, M. C., and J., Rosický (1999). Comparing coequalizer and exact completions. Theory Appl. Categ. 6: 77–82.Google Scholar
Pedicchio, M. C., and F., Rovatti (2004). Algebraic categories. In Categorical Foundations. Cambridge University Press, 269–310.Google Scholar
Pedicchio, M. C., and E. M., Vitale (2000). On the abstract characterization of quasivarieties. Algebra Universalis 43: 269–278.CrossRefGoogle Scholar
Pedicchio, M. C., and R. J., Wood (2000). A simple characterization of theories of varieties. J. Algebra 233: 483–501.CrossRefGoogle Scholar
Popesco, N., and P., Gabriel (1964). Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes. C. R. Acad. Sci. Paris 258: 4188–4190.Google Scholar
Porst, H.-E. (2000). Equivalence for varieties in general and for Bool in particular. Algebra Universalis 43: 157–186.CrossRefGoogle Scholar
Power, J. (1999). Enriched Lawvere theories. Theory Appl. Categ. 6: 83–93.Google Scholar
Rezk, C. W. (1996). Spaces of algebra structures and cohomology of operands. Thesis, MIT.
Roos, J. E. (1965). Caractérisation des catégories qui sont quotients des modules par des sous-catégories bilocalisantes. C. R. Acad. Sci. Paris 261: 4954–4957.Google Scholar
Rosický, J. (2007). On homotopy varieties. Adv. Math. 214: 525–550.CrossRefGoogle Scholar
Rosický, J., and E. M., Vitale (2001). Exact completion and representations in abelian categories. Homology Homotopy Appl. 3: 453–466.CrossRefGoogle Scholar
Schubert, H. (1972). Categories. Springer.CrossRefGoogle Scholar
Street, R. (1974). Elementary cosmoi I. In Category Seminar Sydney. Lect. Notes in Math. 420. Springer, 75–103.Google Scholar
Street, R., and R. F. C., Walters (1978). Yoneda structures on 2-categories. J. Algebra 50: 350–379.CrossRefGoogle Scholar
Tholen, W. (2003). Variations on the Nullstellensatz, paper presented at the European Conference on Category Theory, Haute Bodeux, Belgium.
Ulmer, F. (1968). Properties of dense and relative adjoints. J. Algebra 8: 77–95.CrossRefGoogle Scholar
Vitale, E. M. (1996). Localizations of algebraic categories. J. Pure Appl. Algebra 108: 315–320.CrossRefGoogle Scholar
Vitale, E. M. (1998). Localizations of algebraic categories II. J. Pure Appl. Algebra 133: 317–326.CrossRefGoogle Scholar
Voronov, A. A. (2005). Notes on universal algebra. In Proc. Symp. Pure Math 73. AMS, 81–103.Google Scholar
Watts, C. E. (1960). Intrinsic characterizations of some additive functors. Proc. Amer. Math. Soc. 11: 5–8.CrossRefGoogle Scholar
Wechler, W. (1992). Universal Algebra for Computer Science. Springer.CrossRefGoogle Scholar
Wraith, G. C. (1970). Algebraic Theories. Aarhus Lecture Note Series 22. Aarhus Universitat.Google Scholar

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  • References
  • J. Adámek, Technische Universität Carolo Wilhelmina zu Braunschweig, Germany, J. Rosický, Masarykova Univerzita v Brně, Czech Republic, E. M. Vitale, Université Catholique de Louvain, Belgium
  • Foreword by F. W. Lawvere
  • Book: Algebraic Theories
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511760754.029
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  • References
  • J. Adámek, Technische Universität Carolo Wilhelmina zu Braunschweig, Germany, J. Rosický, Masarykova Univerzita v Brně, Czech Republic, E. M. Vitale, Université Catholique de Louvain, Belgium
  • Foreword by F. W. Lawvere
  • Book: Algebraic Theories
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511760754.029
Available formats
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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • J. Adámek, Technische Universität Carolo Wilhelmina zu Braunschweig, Germany, J. Rosický, Masarykova Univerzita v Brně, Czech Republic, E. M. Vitale, Université Catholique de Louvain, Belgium
  • Foreword by F. W. Lawvere
  • Book: Algebraic Theories
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511760754.029
Available formats
×