@article {
author = {Kachour, Camell},
title = {Combinatorial approach of the category $\Theta_0$ of cubical pasting diagrams},
journal = {Categories and General Algebraic Structures with Applications},
volume = {21},
number = {1},
pages = {19-68},
year = {2024},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.48308/cgasa.2023.104127},
abstract = {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. },
keywords = {Pasting diagrams,pasting schemes,sketch theory,higher order terms},
url = {https://cgasa.sbu.ac.ir/article_104127.html},
eprint = {https://cgasa.sbu.ac.ir/article_104127_f77d5847a666cf26ad9963292d77126e.pdf}
}