TL;DR
This paper introduces duality categories as a broad generalization of duality groups, illustrating their application in Serre duality for polynomial functors and in finite complexes like Tits buildings.
Contribution
It defines the concept of duality categories and demonstrates their relevance through examples such as Serre duality and finite Tits buildings.
Findings
Finite Tits buildings are duality categories.
Serre duality extends to categories of polynomial functors.
Duality categories generalize duality groups.
Abstract
We define the notion of duality categories as generalization of duality groups. Two examples are treated. The first is the Serre duality in the categories of strict polynomial functors. The second concerns finite complexes. We show in particular that finite Tits buildings are duality categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra