%0 Journal Article
%T Combinatorial approach of the category $\Theta_0$ of cubical pasting diagrams
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Kachour, Camell
%D 2024
%\ 07/01/2024
%V 21
%N 1
%P 19-68
%! Combinatorial approach of the category $\Theta_0$ of cubical pasting diagrams
%K Pasting diagrams
%K pasting schemes
%K sketch theory
%K higher order terms
%R 10.48308/cgasa.2023.104127
%X 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.
%U https://cgasa.sbu.ac.ir/article_104127_f77d5847a666cf26ad9963292d77126e.pdf