Multiple categories of general quintets

TL;DR

This paper develops a framework for multiple categories derived from generalized Ehresmann quintets, introducing a structure that encompasses lax, colax, and mixed laxity functors to unify various categorical concepts.

Contribution

It constructs a new class of multiple categories based on generalized Ehresmann quintets, integrating lax, colax, and mixed laxity functors into a unified framework.

Findings

Defines a multiple category with objects as lax multiple categories

Introduces transversal arrows as strict multiple functors

Includes arrows of varying laxity from lax to colax

Abstract

We construct various multiple categories, based on generalised Ehresmann quintets. The main construction is a multiple category whose objects are all the `lax' multiple categories; the transversal arrows are their strict multiple functors while the arrows in a positive direction are multiple functors of a `mixed laxity', varying from the lax ones (in direction 1) to the colax ones (in direction \infty).