Cochain complexes over an endofunctor

Abstract

We introduce the categories of left and right complexes for (additive) endofunctors over an additive category $\mathcal{C}$. These categories unify the definitions of complexes over an additive category and modules over repetitive algebras. Supported by Eilenberg-Moore theory and Happel's successful work, we study the descriptions and properties of these categories, highlighting both similarities and differences with complexes and modules over repetitive algebras. We also examine the influence and interaction of these categories with the category of endofunctors, leading to applications in the representation theory of algebras and with eventual applications in ($2$-)algebraic geometry.

arXiv commentIn this updated version, we have improved the overall presentation as well as several key results and proofs