Separable K-Linear Categories

TL;DR

This paper introduces the concept of separable K-linear categories, demonstrating their local finiteness and projectivity of modules, with applications to categories spanned by groupoids or delta categories.

Contribution

It defines separable K-linear categories and characterizes their structure and properties, extending understanding of their module theory and applications.

Findings

Separable K-linear categories are locally finite.

Every left module over such a category is projective.

Characterizations include categories spanned by groupoids or delta categories.

Abstract

We define and investigate separable K-linear categories. We show that such a category C is locally finite and that every left C-module is projective. We apply our main results to characterize separable linear categories that are spanned by groupoids or delta categories.