Geodesic
Intercategories
Theory and applications of categories, Tome 30 (2015), pp. 1215-1255.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Publié le :
Classification : 18D05, 18D10
Keywords: interchange law, intercategory, triple category, 2-category, double category, lax and colax functor, pseudocategory 
@article{TAC_2015_30_a37,
     author = {Marco Grandis and Robert Par\'e},
     title = {Intercategories},
     journal = {Theory and applications of categories},
     pages = {1215--1255},
     publisher = {mathdoc},
     volume = {30},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a37/}
}
TY  - JOUR
AU  - Marco Grandis
AU  - Robert Paré
TI  - Intercategories
JO  - Theory and applications of categories
PY  - 2015
SP  - 1215
EP  - 1255
VL  - 30
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2015_30_a37/
LA  - en
ID  - TAC_2015_30_a37
ER  - 
%0 Journal Article
%A Marco Grandis
%A Robert Paré
%T Intercategories
%J Theory and applications of categories
%D 2015
%P 1215-1255
%V 30
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2015_30_a37/
%G en
%F TAC_2015_30_a37
Marco Grandis; Robert Paré. Intercategories. Theory and applications of categories, Tome 30 (2015), pp. 1215-1255. http://geodesic.mathdoc.fr/item/TAC_2015_30_a37/