2012/12/05 by Markus Linckelmann · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Functor #Mathematics #Inverse #Cohomology #Pure mathematics #Transfer (computing) #Inverse system #Abelian group #Algebra over a field #Computer science #Geometry
paper · pdf · doi:10.1017/s0013091512000211
openalex publication_date 2012/12/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
Abstract It follows from methods of B. Steinberg, extended to inverse categories, that finite inverse category algebras are isomorphic to their associated groupoid algebras; in particular, they are symmetric algebras with canonical symmetrizing forms.We deduce the existence of transfer maps in cohomology and Hochschild cohomology from certain inverse subcategories. This is in part motivated by the observation that, for certain categories C , being a Mackey functor on C is equivalent to being extendible to a suitable inverse category containing C . We further show that extensions of inverse categories by abelian groups are again inverse categories.