The coherator $\Theta^{\infty}_W$ of cubical weak $\infty$-categories with connections
| Autor: | Camell Kachour |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Categories and General Algebraic Structures with Applications, Vol 21, Iss 1, Pp 69-126 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2345-5853 2345-5861 |
| DOI: | 10.48308/cgasa.2023.104139 |
| Popis: | This work exhibits two applications of the combinatorial approach in [12] of the small category $\Theta_0$ which objects are cubical pasting diagrams. First we provide an accurate description of the monad $\mathbb{S}=(S,\lambda,\mu)$ acting on the category ${\mathbb{C}\mathbb{S}\text{ets}}$ of cubical sets (without degeneracies and connections), which algebras are cubical strict $\infty$-categories with connections, and show that this monad is cartesian, which solve a conjecture in \cite{camark-cub}. Secondly we give a precise construction of the cubical coherator $\Theta^{\infty}_W$ which set-models are cubical weak $\infty$-categories with connections, and we also give a precise construction of the cubical coherator $\Theta^{\infty}_{W^{0}}$ which set-models are cubical weak $\infty$-groupoids with connections. |
| Databáze: | Directory of Open Access Journals |
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