The geometry of cubical and regular transition systems

Philippe Gaucher (1)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

There exist cubical transition systems containing cubes having an arbitrarily large number of faces. A regular transition system is a cubical transition system such that each cube has the good number of faces. The categorical and homotopical results of regular transition systems are very similar to the ones of cubical ones. A complete combinatorial description of fibrant cubical and regular transition systems is given. One of the two appendices contains a general lemma of independant interest about the restriction of an adjunction to a full reflective subcategory.

Mots clés: higher dimensional transition system; left determined model category; weak factorization system; combinatorial model category

Domaines: Mathématiques [math]

Philippe Gaucher. The geometry of cubical and regular transition systems. Cahiers de topologie et géométrie différentielle catégoriques, 2015, LVI (4). ⟨hal-01225836⟩