Discrete vertices in simplicial objects internal to a monoidal category
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917644809011200 |
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| author | Mertens, Arne |
| author_facet | Mertens, Arne |
| contents | We follow the work of Aguiar on internal categories and introduce simplicial objects internal to a monoidal category as certain colax monoidal functors. Then we compare three approaches to equipping them with a discrete set of vertices. We introduce based colax monoidal functors and show that under suitable conditions they are equivalent to the templicial objects defined in arXiv:2302.02484v2. We also compare templicial objects to the enriched Segal precategories appearing in the work of Lurie, Simpson and Bacard, and show that they are equivalent for cartesian monoidal categories, but not in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete vertices in simplicial objects internal to a monoidal category Mertens, Arne Category Theory 18M05, 18N50 We follow the work of Aguiar on internal categories and introduce simplicial objects internal to a monoidal category as certain colax monoidal functors. Then we compare three approaches to equipping them with a discrete set of vertices. We introduce based colax monoidal functors and show that under suitable conditions they are equivalent to the templicial objects defined in arXiv:2302.02484v2. We also compare templicial objects to the enriched Segal precategories appearing in the work of Lurie, Simpson and Bacard, and show that they are equivalent for cartesian monoidal categories, but not in general. |
| title | Discrete vertices in simplicial objects internal to a monoidal category |
| topic | Category Theory 18M05, 18N50 |
| url | https://arxiv.org/abs/2404.12456 |