Intercategories
Abstract
We introduce a 3-dimensional categorical structure which we call intercategory. This is a kind of weak triple category with three kinds of arrows, three kinds of 2-dimensional cells and one kind of 3-dimensional cells. In one dimension, the compositions are strictly associative and unitary, whereas in the other two, these laws only hold up to coherent isomorphism. The main feature is that the interchange law between the second and third compositions does not hold, but rather there is a non invertible comparison cell which satisfies some coherence conditions. We introduce appropriate morphisms of intercategory, of which there are three types, and cells relating these. We show that these fit together to produce a strict triple category of intercategories.
Cite
@article{arxiv.1412.0144,
title = {Intercategories},
author = {Marco Grandis and Robert Paré},
journal= {arXiv preprint arXiv:1412.0144},
year = {2015}
}
Comments
41 pages. New title and material rearranged according to the recommendations of referee. Some added examples. Final version to appear in Theory and Applications of Categories