Misc,
Intercategories I: The basic theory
(2014)cite http://arxiv.org/abs/1412.0144arxiv:1412.0144Comment: 40 pages.
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.
