# A functorial approach to monomorphism categories for species I

## TL;DR

This paper generalizes the concept of monomorphism categories to include species over locally bounded quivers, demonstrating that certain functors preserve almost split sequences, thus enabling explicit computations.

## Contribution

It introduces a broad extension of monomorphism categories and proves the preservation of almost split sequences under specific functors, applicable to generalized species.

## Key findings

- Functorial extension of monomorphism categories for species.
- Preservation of almost split sequences by kernel and cokernel functors.
- Explicit computations remain feasible within the new framework.

## Abstract

We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalised species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor send almost split sequences over the path algebra and the preprojective algebra to split or almost split sequences in the monomorphism category. We derive this from a general result on preservation of almost split morphisms under adjoint functors whose counit is a monomorphism. Despite of its generality, our monomorphism categories still allow for explicit computations as in the case of Ringel and Schmidmeier.