# The tensor product of Gorenstein-projective modules over category algebras

## TL;DR

This paper characterizes when the tensor product of Gorenstein-projective modules over category algebras remains Gorenstein-projective, linking this property to the monomorphism nature of all morphisms in the category.

## Contribution

It establishes a precise condition under which Gorenstein-projective modules are closed under tensor product over category algebras, specifically for finite free and projective EI categories.

## Key findings

- Gorenstein-projective modules are closed under tensor product iff all morphisms are monomorphisms.
- Provides a characterization linking category morphisms to module properties.
- Advances understanding of module behavior over category algebras.

## Abstract

For a finite free and projective EI category, we prove that Gorenstein-projective modules over its category algebra are closed under the tensor product if and only if each morphism in the given category is a monomorphism.