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Homotopy theory of Moore flows (II)

Gaucher, Philippe

Extracta Mathematicae, 2021-12, Vol.36 (2), p.157-239 [Periódico revisado por pares]

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Título:
Homotopy theory of Moore flows (II)
Autor: Gaucher, Philippe
Assuntos: combinatorial model category ; enriched semicategory ; locally presentable category ; Mathematics ; Quillen equivalence ; semimonoidal structure ; topologically enriched category
É parte de: Extracta Mathematicae, 2021-12, Vol.36 (2), p.157-239
Descrição: 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.
Editor: University of Extremadura
Idioma: Inglês

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