On the cohomology rings of small categories
This paper gives generalizations of some theorems in group cohomology theory. Let \(\mathcal C\) denote a small category, \(R\) a commutative ring with identity. Then, the cohomology ring of \(\mathcal C\), with coefficients in \(R\) is defined as the cohomology ring of the topological realization of the nerve of \(\mathcal C\). The author first looks into the cohomology ring modulo nilpotents which he shows is not necessarily finitely generated, even in case of finite EI-category. His springboard are results by Słomińska. The author furthermore studies relationships between the cohomology ring of a category with the cohomology rings of its subcategories and extensions, respectively. The acknowledgments provide an insight into the people who participated in various ways in this project and the appendix provides the reader with standard material regarding the cohomology theory of small categories.
cohomology ring of a small category with coefficients in a commutative ring
scientific article; zbMATH DE number 5321430
scientific article