Thomason cohomology of categories

• Autores: Maria Immaculada Gálvez Carrillo, Frank Neumann, Andrew Tonks
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 217, Nº 11, 2013, págs. 2163-2179
• Idioma: inglés
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• Resumen

  • 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.