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Comparaison de deux catégories d’homotopie de morphismes cohérents. (Comparison of two homotopy categories of coherent morphisms). (French) Zbl 0679.55006

Summary: The homotopy category of coherent morphisms between functors from A to Top defined by Vogt is proved to be isomorphic to a homotopy category of coherent morphisms in which the coherence conditions are simplicially expressed. This latter homotopy category, which is linked to the coherent prohomotopy category of Lisica-Mardesič, is obtained as the Kleisli category of an idempotent comonad on the homotopy category \(\pi_ 0(Top^ A_ s)\) of natural homotopy classes of transformations between functors from A to Top.

MSC:

55P47 Infinite loop spaces
55U35 Abstract and axiomatic homotopy theory in algebraic topology
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References:

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