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

2025/10/27 by Gulisz, Vitor, Rump, Wolfgang
#16E10 #18E05 #18G20 #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2510.23369

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.

Citations

• A functorial approach to 0-abelian categories
• A functorial approach to n-abelian categories

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