Representation Type of EI-Categories
Karsten Dietrich
TL;DR
This paper investigates the representation type of EI-categories, which generalize finite groups and quivers, providing characterizations for special cases and a necessary criterion for categories with two objects.
Contribution
It offers a complete characterization for certain EI-categories and introduces a necessary criterion for finite representation type in two-object cases.
Findings
Complete characterization for special classes of EI-categories.
Necessary criterion for finite representation type with two objects.
Illustrative examples demonstrating classification complexity.
Abstract
EI-categories are a simultaneous generalisation of finite groups and finite quivers without oriented cycles. It is therefore a natural question to ask for a characterisation of finite representation type. For special classes of EI-categories a complete characterisation is obtained using quiver techniques. For EI-categories with two objects we present a necessary criterion for finite representation type. The complexity of this classification problem is illustrated by some examples.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology