Università degli Studi di Genova


Limits in multiple categories (On weak and lax multiple categories, II)

Continuing our first paper in this series, we study multiple limits in infinite- dimensional multiple categories. The general setting is chiral multiple categories - a weak, partially lax form with directed interchanges. After defining multiple limits we prove that all of them can be constructed from (multiple) products, equalisers and tabulators - all of them assumed to be respected by faces and degeneracies. Tabulators appear thus to be the basic higher limits, as was already the case for double categories. Intercategories, a laxer form of multiple category already studied in two previous papers, are also considered. In this more general setting the basic multiple limits mentioned above can still be defined, but their general theory is not developed here.

multiple category, double category, cubical set, limit.