Classification of grouplike categories
Najwa Ghannoum
TL;DR
This paper investigates grouplike monoids, classifies finite categories with two objects having such monoids, and counts specific categories with grouplike structures, advancing understanding of their algebraic properties.
Contribution
It provides a classification of finite categories with two objects and grouplike endomorphism monoids, and offers enumeration results for related categories.
Findings
Classification of finite categories with two objects having grouplike endomorphism monoids
Counting of certain categories with grouplike monoids
Structural insights into grouplike monoids in categorical contexts
Abstract
In this paper we study grouplike monoids, these are monoids that contain a group to which we add an ordered set of idempotents. We classify finite categories with two objects having grouplike endomorphism monoids, and we give a count of certain categories with grouplike monoids.
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Taxonomy
TopicsRings, Modules, and Algebras · semigroups and automata theory