Università degli Studi di Genova


Limits in symmetric cubical categories (On weak cubical categories, II)

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.

Weak cubical category, weak double category, cubical set, symmetries

18, 55

Pubblicato su: Cahiers de Topologie et Geometrie Differentielle Categoriques Vol. 50 (2009) Pag. 242-272