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On inverse categories and transfer in cohomology

Linckelmann, M. (2013). On inverse categories and transfer in cohomology. Proceedings of the Edinburgh Mathematical Society, 56(1), pp. 187-210. doi: 10.1017/S0013091512000211


It follows from methods of B. Steinberg [22], extended to inverse categories, that finite inverse category algebras are isomorphic to their associated groupoid algebras; in particular, they are symmetric algebras with canonical symmetrising 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 show further that extensions of inverse categories by abelian groups are again inverse categories.

Publication Type: Article
Additional Information: This article has been accepted for publication and will appear in a revised form, subsequent to peer review and/or editorial input by Cambridge University Press, in Proceedings of the Edinburgh Mathematical Society (Series 2) / Volume 56 / Issue 01 / February 2013, pp 187-210, Copyright Edinburgh Mathematical Society 2013.
Publisher Keywords: Inverse category, transfer, cohomology
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology
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