Some Remarks on the Interchange in Gray-categories

TL;DR

This paper proves a generalized interchange equality for 3-cells in Gray-categories, showing it holds up to a specific isomorphism, which simplifies calculations in this mathematical framework.

Contribution

It introduces a generalized interchange equality in Gray-categories that accounts for the isomorphism from the Gray-categorical pasting theorem, simplifying complex calculations.

Findings

Proves a generalized interchange equality for 3-cells in Gray-categories.

Shows the equality holds modulo a unique isomorphism.

Simplifies calculations in Gray-categories.

Abstract

We prove a generalised interchange equality for 3-cells in a Gray-category, i.e. we show that it still holds modulo the unique isomorphism given by the Gray-categorical pasting theorem of Di Vittorio. This significantly simplifies many calculations in Gray-categories.