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- Title
On inverse categories and transfer in cohomology.
- Authors
Linckelmann, Markus
- 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 $\mathcal{C}$, being a Mackey functor on $\mathcal{C}$ is equivalent to being extendible to a suitable inverse category containing $\mathcal{C}$. We further show that extensions of inverse categories by abelian groups are again inverse categories.
- Subjects
INVERSE functions; CATEGORIES (Mathematics); COHOMOLOGY theory; TRANSFER (Algebraic topology); ABELIAN groups; MATHEMATICAL symmetry; ISOMORPHISM (Mathematics)
- Publication
Proceedings of the Edinburgh Mathematical Society, 2013, Vol 56, Issue 1, p187
- ISSN
0013-0915
- Publication type
Article
- DOI
10.1017/S0013091512000211