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 additive 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.

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