Combinatorial approach of the category $\Theta_0$ of cubical pasting diagrams
| Autor: | Camell Kachour |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Categories and General Algebraic Structures with Applications, Vol 21, Iss 1, Pp 19-68 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2345-5853 2345-5861 |
| DOI: | 10.48308/cgasa.2023.104127 |
| Popis: | In globular higher category theory the small category $\Theta_0$ of finite rooted trees plays an important role: for example the objects of $\Theta_0$ are the arities of the operations inside the free globular $\omega$-operad $\mathbb{B}^0$ of Batanin, which $\mathbb{B}^0$-algebras are models of globular weak $\infty$-categories; also this globular $\Theta_0$ is an important tool to build the coherator $\Theta^{\infty}_{W^0}$ of Grothendieck which ${\mathbb{S}\text{ets}}$-models are globular weak $\infty$-groupoids. Cubical higher category needs similarly its $\Theta_0$. In this work we describe, combinatorially, the small category $\Theta_0$ which objects are cubical pasting diagrams and which morphisms are morphisms of cubical sets. |
| Databáze: | Directory of Open Access Journals |
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