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Applied Categorical Structures

, Volume 13, Issue 5–6, pp 371–388 | Cite as

Flow does not Model Flows up to Weak Dihomotopy

  • Philippe GaucherEmail author
Article

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.

Keywords

concurrency homotopy weak factorizarion system cofibrantly generated modelcategory locally presentable model category combinatorial model category directed homotopy 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Preuves Programmes et SystèmesUniversit˝ Paris 7-Denis DiderotParis Cedex 05France

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