Thomason cohomology of categories. (English) Zbl 1285.18020
This paper is about a new cohomology theory for small categories called Thomason cohomology. The coefficients for the cohomology of a small category \({\mathcal C}\) in this theory are functors on the comma category \(\Delta/{\mathcal C}\), where \(\Delta\) is the simplex category. The theory generalises Baues-Wirsching cohomology. There is a dual Thomason homology theory generalising Baues-Wirsching homology theory. The Thomason cohomology and homology theories of \({\mathcal C}\) coincide with Gabriel-Zisman cohomology and homology of the simplicial nerve of \({\mathcal C}\). In certain situations there are Leray-type spectral sequences.
Reviewer: Richard John Steiner (Glasgow)
MSC:
| 18G60 | Other (co)homology theories (MSC2010) |
| 18G40 | Spectral sequences, hypercohomology |
| 18D30 | Fibered categories |
| 55U10 | Simplicial sets and complexes in algebraic topology |
Keywords:
Thomason cohomology; Thomason homology; Baues-Wirsching cohomology; Baues-Wirsching homology; Gabriel-Zisman cohomology; Gabriel-Zisman homologyReferences:
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