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

Vitor Gulisz; Wolfgang Rump

doi:10.1007/s00013-026-02238-x

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arXiv · 2510.23369

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

Vitor Gulisz·Wolfgang Rump

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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.

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Vitor Gulisz, Wolfgang Rump. 2025-10-27. On the equivalence between the existence of $n$-kernels and $n$-cokernels. https://doi.org/10.1007/s00013-026-02238-x

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