Università degli Studi di Genova


Adjoints for symmetric cubical categories (On weak cubical categories, III)

Extending a previous article on adjoints for double categories, we deal here with weak symmetric cubical categories (of infinite dimension). Also here, a general 'cubical adjunction' has a colax cubical functor left adjoint to a lax one. This cannot be viewed as an adjunction in some bicategory, because composing lax and colax morphisms destroys all comparisons. However, as in the case of double adjunctions, cubical adjunctions live in an interesting double category; this now consists of weak symmetric cubical categories, with lax and colax double functors as horizontal and vertical arrows, linked by suitable double cells.

weak cubical category, weak double category, adjoint functor, cubical set, symmetries


Pubblicato su: Cahiers de Topologie et Geometrie Differentielle Categoriques Vol. 54 (2013) Pag. 91-126