Categories enriched over symmetric closed multicategories
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866910671461941248 |
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| author | Lyubashenko, Volodymyr |
| author_facet | Lyubashenko, Volodymyr |
| contents | We construct a machine which takes as input a locally small symmetric closed complete multicategory $\mathsf V$. And its output is again a locally small symmetric closed complete multicategory $\mathsf V\text-\mathcal{C}at$, the multicategory of small $\mathsf V$-categories and multi-entry $\mathsf V$-functors.
An example of such $\mathsf V$ is provided by short spaces (vector spaces with a system of seminorms) and short maps. When the ground multicategory $\mathsf V$ is $\mathsf{Set}$ we obtain strict 2-categories and their surroundings by iterating twice the construction of categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11227 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Categories enriched over symmetric closed multicategories Lyubashenko, Volodymyr Category Theory 18M65 We construct a machine which takes as input a locally small symmetric closed complete multicategory $\mathsf V$. And its output is again a locally small symmetric closed complete multicategory $\mathsf V\text-\mathcal{C}at$, the multicategory of small $\mathsf V$-categories and multi-entry $\mathsf V$-functors. An example of such $\mathsf V$ is provided by short spaces (vector spaces with a system of seminorms) and short maps. When the ground multicategory $\mathsf V$ is $\mathsf{Set}$ we obtain strict 2-categories and their surroundings by iterating twice the construction of categories. |
| title | Categories enriched over symmetric closed multicategories |
| topic | Category Theory 18M65 |
| url | https://arxiv.org/abs/2304.11227 |