Flow does not model flows up to weak dihomotopy

Philippe Gaucher (1)

1 PPS - Preuves, Programmes et Systèmes

We prove that the category of flows cannot be the underlying category of a model category whose corresponding homotopy types are the flows up to weak dihomotopy. Some hints are given to overcome this problem. In particular, a new approach of dihomotopy involving simplicial presheaves over an appropriate small category is proposed. This small category is obtained by taking a full subcategory of a locally presentable version of the category of flows.

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]

Philippe Gaucher. Flow does not model flows up to weak dihomotopy. Applied Categorical Structures, 2005, 13 (5-6), pp.371-388. ⟨hal-00150921⟩