On duoidal $\infty$-categories
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910798617509888 |
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| author | Torii, Takeshi |
| author_facet | Torii, Takeshi |
| contents | A duoidal category is a category equipped with two monoidal structures in which one is (op)lax monoidal with respect to the other. In this paper we introduce duoidal $\infty$-categories which are counterparts of duoidal categories in the setting of $\infty$-categories. There are three kinds of functors between duoidal $\infty$-categories, which are called bilax, double lax, and double oplax monoidal functors. We make three formulations of $\infty$-categories of duoidal $\infty$-categories according to which functors we take. Furthermore, corresponding to the three kinds of functors, we define bimonoids, double monoids, and double comonoids in duoidal $\infty$-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_14121 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On duoidal $\infty$-categories Torii, Takeshi Category Theory Algebraic Topology 18N70 (primary), 18N60, 18N50, 55U40 (secondary) A duoidal category is a category equipped with two monoidal structures in which one is (op)lax monoidal with respect to the other. In this paper we introduce duoidal $\infty$-categories which are counterparts of duoidal categories in the setting of $\infty$-categories. There are three kinds of functors between duoidal $\infty$-categories, which are called bilax, double lax, and double oplax monoidal functors. We make three formulations of $\infty$-categories of duoidal $\infty$-categories according to which functors we take. Furthermore, corresponding to the three kinds of functors, we define bimonoids, double monoids, and double comonoids in duoidal $\infty$-categories. |
| title | On duoidal $\infty$-categories |
| topic | Category Theory Algebraic Topology 18N70 (primary), 18N60, 18N50, 55U40 (secondary) |
| url | https://arxiv.org/abs/2106.14121 |