Resumen de Thomason cohomology of categories

Maria Immaculada Gálvez Carrillo , Frank Neumann, Andrew Tonks

• 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.