A reference for categorical structures on $\mathbf{Poly}$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909807124938752 |
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| author | Spivak, David I. |
| author_facet | Spivak, David I. |
| contents | In this document, we collect a list of categorical structures on the category $\mathbf{Poly}$ of polynomial functors. There is no implied claim that this list is in any way complete. It includes: infinitely many monoidal structures, all but one of which is symmetric, closed, and distributes over $+$, several of which interact duoidally; it also includes a right-coclosure and two indexed left coclosures; it also includes various adjunctions of which $\mathbf{Poly}$ is a part, including the free monad and cofree comonad and their interaction with various monoidal structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_00534 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A reference for categorical structures on $\mathbf{Poly}$ Spivak, David I. Category Theory 18A25, 18M05 In this document, we collect a list of categorical structures on the category $\mathbf{Poly}$ of polynomial functors. There is no implied claim that this list is in any way complete. It includes: infinitely many monoidal structures, all but one of which is symmetric, closed, and distributes over $+$, several of which interact duoidally; it also includes a right-coclosure and two indexed left coclosures; it also includes various adjunctions of which $\mathbf{Poly}$ is a part, including the free monad and cofree comonad and their interaction with various monoidal structures. |
| title | A reference for categorical structures on $\mathbf{Poly}$ |
| topic | Category Theory 18A25, 18M05 |
| url | https://arxiv.org/abs/2202.00534 |