Transport of structure in higher homological algebra
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866917755378204672 |
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| author | Bennett-Tennenhaus, Raphael Shah, Amit |
| author_facet | Bennett-Tennenhaus, Raphael Shah, Amit |
| contents | We fill a gap in the literature regarding `transport of structure' for (n+2)-angulated, n-exact, n-abelian and n-exangulated categories appearing in (classical and higher) homological algebra. As an application of our main results, we show that a skeleton of one of these kinds of categories inherits the same structure in a canonical way, up to equivalence. In particular, it follows that a skeleton of a weak (n+2)-angulated category is in fact what we call a strong (n+2)-angulated category. When n=1 this clarifies a technical concern with the definition of a cluster category. We also introduce the notion of an n-exangulated functor between n-exangulated categories. This recovers the definition of an (n+2)-angulated functor when the categories concerned are (n+2)-angulated, and the higher analogue of an exact functor when the categories concerned are n-exact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_02254 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Transport of structure in higher homological algebra Bennett-Tennenhaus, Raphael Shah, Amit Category Theory Representation Theory 18E05, 18E10, 18G80 We fill a gap in the literature regarding `transport of structure' for (n+2)-angulated, n-exact, n-abelian and n-exangulated categories appearing in (classical and higher) homological algebra. As an application of our main results, we show that a skeleton of one of these kinds of categories inherits the same structure in a canonical way, up to equivalence. In particular, it follows that a skeleton of a weak (n+2)-angulated category is in fact what we call a strong (n+2)-angulated category. When n=1 this clarifies a technical concern with the definition of a cluster category. We also introduce the notion of an n-exangulated functor between n-exangulated categories. This recovers the definition of an (n+2)-angulated functor when the categories concerned are (n+2)-angulated, and the higher analogue of an exact functor when the categories concerned are n-exact. |
| title | Transport of structure in higher homological algebra |
| topic | Category Theory Representation Theory 18E05, 18E10, 18G80 |
| url | https://arxiv.org/abs/2003.02254 |