@article {
author = {Kachour, Camell},
title = {The coherator $\Theta^{\infty}_W$ of cubical weak $\infty$-categories with connections},
journal = {Categories and General Algebraic Structures with Applications},
volume = {21},
number = {1},
pages = {69-126},
year = {2024},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.48308/cgasa.2023.104139},
abstract = {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. },
keywords = {Cubical $\infty$-categories,cubical coherators,Grothendieck approach of cubical weak $\infty$-categories},
url = {https://cgasa.sbu.ac.ir/article_104139.html},
eprint = {https://cgasa.sbu.ac.ir/article_104139_624697552a25e8bee0393e08ecf9ddf6.pdf}
}