The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918148213571584 |
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| author | Dutta, Arghan Luneia, Stefano Rovelli, Martina Silver, Sam |
| author_facet | Dutta, Arghan Luneia, Stefano Rovelli, Martina Silver, Sam |
| contents | We provide an explicit and elementary construction of the Morita $(\infty,2)$-category of a monoidal category which satisfies minimal conditions. We construct it as a $3$-coskeletal $2$-complicial set, in which the vertices encode the monoids, the edges encode the bimodules, the triangles encode the bimodule maps out of a balanced tensor product, and tetrahedra encode composition of bimodule maps. The marked edges encode invertible bimodules, and the marked triangles encode bimodule isomorphisms with a balanced tensor product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21472 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set Dutta, Arghan Luneia, Stefano Rovelli, Martina Silver, Sam Category Theory Algebraic Topology We provide an explicit and elementary construction of the Morita $(\infty,2)$-category of a monoidal category which satisfies minimal conditions. We construct it as a $3$-coskeletal $2$-complicial set, in which the vertices encode the monoids, the edges encode the bimodules, the triangles encode the bimodule maps out of a balanced tensor product, and tetrahedra encode composition of bimodule maps. The marked edges encode invertible bimodules, and the marked triangles encode bimodule isomorphisms with a balanced tensor product. |
| title | The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2509.21472 |