Flow does not model flows up to weak dihomotopy

Abstract

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.

v2 16 pages, 3 figures ; updated bibliography + slight improvements and corrections of typos ; v3 only the Journal-ref field

References in corpus (2)

• Sheafifiable homotopy model categories
• A model category for the homotopy theory of concurrency

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