Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-18T06:06:59.707Z Has data issue: false hasContentIssue false

Morita cohomology and homotopy locally constant sheaves

Published online by Cambridge University Press:  01 December 2014

JULIAN V. S. HOLSTEIN*
Affiliation:
Christ's College, Cambridge, CB2 3BU, United Kingdom e-mail: J.V.S.Holstein@dpmms.cam.ac.uk

Abstract

We identify Morita cohomology, which is a categorification of the cohmology of a topological space X, with the category of homotopy locally constant sheaves of perfect complexes on X.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Barwick, C. On (enriched) left Bousfield localisation of model categories. Arxiv e-prints, (2007), 0708.2067.Google Scholar
[2]Barwick, C. On the dreaded right Bousfield localisation. ArXiv e-prints, (2007), 0708.343.Google Scholar
[3]Barwick, C.On left and right model categories and left and right Bousfield localisations. Homology Homotopy Appl. 12 (2010), pp. 245320.CrossRefGoogle Scholar
[4]Bergner, J. E. Homotopy fiber products of homotopy theories. ArXiv e-prints, (2008), 0811.3175.Google Scholar
[5]Bergner, J. E. Homotopy limits of model categories and more general homotopy theories. ArXiv e-prints, (2010), 1010.0717.Google Scholar
[6]Dwyer, W. G., Greenlees, J. P. C. and Iyengar, S. Duality in algebra and topology. ArXiv e-prints, (2005), 0510247.Google Scholar
[7]Dwyer, W. G., Kan, D. M. and Smith, J. H.Homotopy commutative diagrams and their realizations. Journal of Pure and Applied Algebra. 57 (1989), pp. 524.CrossRefGoogle Scholar
[8]Fritsch, R. and Piccinini, R.Cellular Structures in Topology. Cambridge Stud. Adv. Math. vol. 19 (Cambridge University Press, 1990).Google Scholar
[9]Hirschowitz, A. and Simpson, C. Descente pour les n-champs. Arxiv e-prints, (2001), math/9807049.Google Scholar
[10]Holstein, J. V. S. Morita cohomology. PhD. thesis. University of Cambridge (2014).CrossRefGoogle Scholar
[11]Holstein, J. V. S. Morita cohomology. ArXiv e-prints, (2014), 1404.1327.Google Scholar
[12]Kelly, G.Basic Concepts of Enriched Category Theory. London Mathematical Society Lecture Notes. 64 (Cambridge University Press, 1982).Google Scholar
[13]Lurie, J. Higher Algebra. Available at www.math.harvard.edu/lurie/papers/higheralgebra.pdf. (April 2011).Google Scholar
[14]Spitzweck, M.Homotopy limits of model categories over inverse index categories. J. Pure Appl. Algebra 214 (2010), pp. 769777.Google Scholar
[15]Stacks, T. Project Authors. Stacks project. http://stacks.math.columbia.edu, 2013.Google Scholar
[16]Toën, B. and Vezzosi, G. Segal topoi and stacks over Segal categories. ArXiv e-prints, (2002), math.AG/0212330.Google Scholar
[17]Toën, B. and Vezzosi, G. Homotopical algebraic geometry II: geometric stacks and applications. ArXiv e-prints, (2004), math.AG/0404373.Google Scholar