Preprint: Limits in symmetric cubical categories

Preprint: Limits in symmetric cubical categories

[Marco Grandis]

The following preprint is available;

Limits in symmetric cubical categories
(On weak cubical categories, II)
Dip. Mat. Univ. Genova, Preprint 568 (2009).  (25 pages)
    http://www.dima.unige.it/~grandis/CCat2.pdf  (ps)

Abstract. Weak symmetric cubical categories are equipped with
an action of the n-dimensional symmetric group on the n-dimensional
component; this action, besides simplifying the coherence conditions,
yields a *symmetric* monoidal closed structure and one path functor.
As a consequence, we have a clear notion of higher cubical
transformations of symmetric cubical functors (which is not the case
in the non-symmetric setting).

    Here we deal with symmetric cubical limits, showing that they can be
constructed from symmetric cubical products, equalisers and tabulators.
Weak double categories are a cubical truncation of the present
structures;
double limits are compared with the cubical ones.

With best wishes

Marco Grandis