$2$-Categories from a Gray Perspective

Edward Morehouse

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arXiv · 2203.08783

$2$-Categories from a Gray Perspective

Edward Morehouse

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Abstract

In this paper we present $2$-category theory from the perspective of Gray-categories using the graphical calculus of separated surface diagrams. As an extended example we consider cones and limits of $2$-functors. Then we use the canonical adjunction between $2$-computads and $2$-categories to interpret the comparison structure of lax functors and extend the surface diagram calculus with compositor sheets in order to represent and reason about them.

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Edward Morehouse. 2022-03-16. $2$-Categories from a Gray Perspective. https://arxiv.org/abs/2203.08783

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