We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues-Wirsching cohomology and homology of a small category, and coincide with Gabriel-Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues-Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories. (C) 2013 Elsevier B.V. All rights reserved.
Thomason cohomology of categories
Neumann, F
;
2013-01-01
Abstract
We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues-Wirsching cohomology and homology of a small category, and coincide with Gabriel-Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues-Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories. (C) 2013 Elsevier B.V. All rights reserved.File in questo prodotto:
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