On the equivalence between the existence of $n$-kernels and $n$-cokernels
Category Theory
2026-05-25 v2 Rings and Algebras
Representation Theory
Abstract
We give an elementary proof of the statement that if an idempotent complete preadditive category has weak kernels and weak cokernels, then it has -kernels if and only if it has -cokernels, where is a nonnegative integer. As a consequence, elementary proofs of two results concerning the equality between the global dimensions of certain right and left module categories are obtained.
Cite
@article{arxiv.2510.23369,
title = {On the equivalence between the existence of $n$-kernels and $n$-cokernels},
author = {Vitor Gulisz and Wolfgang Rump},
journal= {arXiv preprint arXiv:2510.23369},
year = {2026}
}
Comments
6 pages. v2: added a paragraph in the introduction section; added a preliminaries section; accepted for publication in Arch. Math. (Basel)