Intercategories

Understand

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.