Preprint: Limits in multiple categories

Preprint: Limits in multiple categories

[Marco Grandis]

There is now a second preprint in our series on multiple categories:

M. Grandis - R. Paré
Limits in multiple categories (On weak and lax multiple categories, II)
Pubbl. Mat. Univ. Genova, Preprint 605 (2015).
http://www.dima.unige.it/~grandis/Mlc2.pdf

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.

The first paper of the series is:
M. Grandis - R. Paré
An introduction to multiple categories (On weak and lax multiple  
categories, I)
Pubbl. Mat. Univ. Genova, Preprint 604 (2015).
http://www.dima.unige.it/~grandis/Mlc1.pdf

Marco Grandis and Bob Paré






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