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

Vitor Gulisz; Wolfgang Rump

doi:10.1007/s00013-026-02238-x

April 17, 2026Archiv der MathematikOpen Access

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

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Key Points

The research aims to prove that in certain categories, the existence of n-kernels directly corresponds to the existence of n-cokernels.
Provided an elementary proof using foundational category theory concepts.
Considered idempotent complete preadditive categories with weak kernels and cokernels.
Analyzed the implications for global dimensions of module categories.
Established that n-kernels exist if and only if n-cokernels exist for nonnegative integers n.
Derived additional results related to the equality of global dimensions in specific module categories.

Implication

This article demonstrates the equivalence of n-kernels and n-cokernels in idempotent complete categories, indicating deeper mathematical relationships.

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Cite This Study

Gulisz et al. (2026) studied this question.

synapsesocial.com/papers/69e31ff140886becb653f18c https://doi.org/10.1007/s00013-026-02238-x

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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