The tensor product of Gorenstein-projective modules 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.

KEYWORDS:

• Category algebra
• finite EI category
• Gorenstein-projective module
• tensor product
• tensor triangulated category

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16G10
• Secondary 16D90, 18E30

Acknowledgements

The author thanks the referee for helpful comments. The author is grateful to her supervisor Professor Xiao-Wu Chen for his guidance.