Twisted Commutators and Internal Crossed Modules
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909340882960384 |
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| author | Deval, Bo Shan Van der Linden, Tim |
| author_facet | Deval, Bo Shan Van der Linden, Tim |
| contents | We introduce a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity -- also obtained as a modification of the usual notion -- and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07489 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Twisted Commutators and Internal Crossed Modules Deval, Bo Shan Van der Linden, Tim Category Theory 18D40, 18E13, 18G45 We introduce a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity -- also obtained as a modification of the usual notion -- and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category. |
| title | Twisted Commutators and Internal Crossed Modules |
| topic | Category Theory 18D40, 18E13, 18G45 |
| url | https://arxiv.org/abs/2311.07489 |