Middle-Four Maps and Net Categories

TL;DR

This paper explores the relationship between middle-four interchange maps in categories with two monoidal structures and the concept of weakly distributive categories, highlighting their theoretical connection.

Contribution

It establishes a link between middle-four maps and weakly distributive categories, clarifying their conceptual relationship.

Findings

Middle-four maps relate to weakly distributive categories.

The paper clarifies the theoretical connection between these structures.

It provides a categorical framework linking two monoidal structures.

Abstract

We briefly relate the existence of a middle-four interchange map in a category with two monoidal structures, to the standard Cockett and Seely notion of a weakly distributive category.