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.
CitationGalvez, M.; Neumann, F.; Tonks, A. Thomason cohomology of categories. "Journal of pure and applied algebra", 2013, vol. 217, núm. 11, p. 2163-2179.
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