Free and co-free constructions for Hopf categories
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910427783364608 |
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| author | Großkopf, Paul Vercruysse, Joost |
| author_facet | Großkopf, Paul Vercruysse, Joost |
| contents | We show that under mild conditions on the monoidal base category $\mathcal V$, the category ${\sf VHopf}$ of Hopf $\mathcal V$-categories is locally presentable and deduce the existence of free and cofree Hopf categories. We also provide an explicit description of the free and cofree Hopf categories over a semi-Hopf category. One of the conditions on the base category $\mathcal V$, states that endofunctors obtained by tensoring with a fixed object preserve jointly monic families, which leads us to the notion of ``very flat monoidal product'', which we investigate in particular for module categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03120 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Free and co-free constructions for Hopf categories Großkopf, Paul Vercruysse, Joost Category Theory Rings and Algebras We show that under mild conditions on the monoidal base category $\mathcal V$, the category ${\sf VHopf}$ of Hopf $\mathcal V$-categories is locally presentable and deduce the existence of free and cofree Hopf categories. We also provide an explicit description of the free and cofree Hopf categories over a semi-Hopf category. One of the conditions on the base category $\mathcal V$, states that endofunctors obtained by tensoring with a fixed object preserve jointly monic families, which leads us to the notion of ``very flat monoidal product'', which we investigate in particular for module categories. |
| title | Free and co-free constructions for Hopf categories |
| topic | Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2305.03120 |