Year: 2022
Type: preprint
Abstract: The notion of $\textbf{Gray}$-category, a semi-strict $3$-category in which the middle four interchange is weakened to an isomorphism, is central in the study of three-dimensional category theory. In this context it is common practice to use $2$-dimensional pasting diagrams to express composites of $2$-cells, however there is no thorough treatment in the literature justifying this procedure. We fill this gap by providing a formal approach to pasting in $\textbf{Gray}$-categories and by proving that such composites are uniquely defined up to a contractible groupoid of choices.
Source: arXiv (Cornell University)
Author: Di Vittorio, Nicola
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4281717816