Abstract:
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.
Keywords:
multiple category, double category, cubical set, limit.
MSC:
18
