A Gray-categorical pasting theorem

Nicola Di Vittorio

The notion of 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 Gray-categories and by proving that such composites are uniquely defined up to a contractible groupoid of choices.

Keywords: Gray-categories, pasting diagrams

2020 MSC: 18N20, 16S15, 03E20

Theory and Applications of Categories, Vol. 39, 2023, No. 5, pp 150-171.

Published 2023-02-01.


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