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<p>We give an elementary proof of the statement that if an idempotent complete preadditive category has weak kernels and weak cokernels, then it has <i>n</i>-kernels if and only if it has <i>n</i>-cokernels, where <i>n</i> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月17日

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  • Vitor Gulisz,
  • Wolfgang Rump

摘要

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.