Intercategories: A framework for three-dimensional category theory
Category Theory
2016-07-12 v3
Abstract
We show how the notion of intercategory encompasses a wide variety of three-dimensional structures from the literature, notably duoidal categories, monoidal double categories, cubical bicategories, double bicategories and Gray categories. Variations on the notion of span provide further examples of interest, an important one being the intercategory of sets. We consider the three kinds of morphism of intercategory as well as the cells binding them with applications to the above structures. In particular hom functors are studied.
Cite
@article{arxiv.1412.0212,
title = {Intercategories: A framework for three-dimensional category theory},
author = {Robert Paré and Marco Grandis},
journal= {arXiv preprint arXiv:1412.0212},
year = {2016}
}
Comments
Revised and expanded following referee's comments (67 pages)