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Article Dans Une Revue Extracta Mathematicae Année : 2021

Homotopy theory of Moore flows (II)

Résumé

This paper proves that the q-model structures of Moore flows and of multipointed $d$-spaces are Quillen equivalent. The main step is the proof that the counit and unit maps of the Quillen adjunction are isomorphisms on the q-cofibrant objects (all objects are q-fibrant). As an application, we provide a new proof of the fact that the categorization functor from multipointed $d$-spaces to flows has a total left derived functor which induces a category equivalence between the homotopy categories. The new proof sheds light on the internal structure of the categorization functor which is neither a left adjoint nor a right adjoint. It is even possible to write an inverse up to homotopy of this functor using Moore flows.
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Dates et versions

hal-03215805 , version 1 (01-10-2021)
hal-03215805 , version 2 (08-11-2021)
hal-03215805 , version 3 (15-11-2021)

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Citer

Philippe Gaucher. Homotopy theory of Moore flows (II). Extracta Mathematicae, 2021, 36 (2), pp.157-239. ⟨10.17398/2605-5686.36.2.157⟩. ⟨hal-03215805v3⟩
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