Flow does not Model Flows up to Weak Dihomotopy

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. Contents

• Type: Journal
• Year: 2005
• Where: ACS
• Authors: Philippe Gaucher
• Keywords: ACS 2005, ACS 2007, Appropriate Small Category, Model Category, Small Category