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

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.