On the equivalence between the existence of $n$-kernels and $n$-cokernels

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 $n$-kernels if and only if it has $n$-cokernels, where $n$ 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.

6 pages. v2: added a paragraph in the introduction section; added a preliminaries section; accepted for publication in Arch. Math. (Basel)

References in corpus (1)

• A functorial approach to $n$-abelian categories