$2$-Categories from a Gray Perspective
Edward Morehouse

TL;DR
This paper explores 2-category theory through Gray-categories and surface diagrams, providing new graphical tools to understand cones, limits, and lax functors in higher category theory.
Contribution
It introduces a graphical calculus for Gray-categories, extending surface diagrams with compositor sheets to analyze lax functors and their comparison structures.
Findings
Graphical calculus effectively represents 2-categories and Gray-categories.
Extended surface diagrams facilitate reasoning about cones and limits of 2-functors.
New interpretation of lax functors using compositor sheets enhances understanding.
Abstract
In this paper we present -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 -functors. Then we use the canonical adjunction between -computads and -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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis
