On the equivalence between the existence of $n$-kernels and $n$-cokernels
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911705976537088 |
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| author | Gulisz, Vitor Rump, Wolfgang |
| author_facet | Gulisz, Vitor Rump, Wolfgang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the equivalence between the existence of $n$-kernels and $n$-cokernels Gulisz, Vitor Rump, Wolfgang Category Theory Rings and Algebras Representation Theory 18E05, 18G20, 16E10 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. |
| title | On the equivalence between the existence of $n$-kernels and $n$-cokernels |
| topic | Category Theory Rings and Algebras Representation Theory 18E05, 18G20, 16E10 |
| url | https://arxiv.org/abs/2510.23369 |