Galois and universal universal coverings of linear categories and fibre products

TL;DR

This paper investigates coverings of linear categories over a commutative ring, providing criteria for when such coverings are Galois or universal, and analyzing their behavior through fibre products.

Contribution

It introduces new criteria for Galois and universal coverings of $k$-categories and explores their properties via fibre product constructions.

Findings

Established a criterion for Galois coverings.

Characterized universal coverings in the context of $k$-categories.

Analyzed the behavior of coverings under fibre products.

Abstract

Let $k$ be a commutative ring. We study the behaviour of coverings of $k$-categories through fibre products and find a criterion for a covering to be Galois or universal.