An introduction to monomorphism categories

Abstract

This work can be divided into four parts: The first part is an introduction to the theory of monomorphism categories, including a short survey on some representation theoretic results. The second part is a summary of some of the main results by Gao, Külshammer, Kvamme, and Psaroudakis (2024) on monomorphism categories. It also includes a new result, namely a classification of all monomorphism categories of finite type over cyclic abelian groups. The third part concerns the relationship between submodule categories and $p$-valuated abelian groups. The last part contains a proof of wildness of a certain monomorphism category, rectifying a statement in the literature.