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Title: Homotopy theory of Moore ows (II)
Authors: Gaucher, P.
Keywords: Enriched semicategory;Semimonoidal structure;Combinatorial model category;Quillen equivalence;Locally presentable category;Topologically enriched category;Moore path;Semicategoría enriquecida;Estructura semimonoidal;Categoría de modelo combinatorio;Quillen equivalencia;Categoría presentable localmente;Categoría enriquecida topológicamente;Camino de Moore
Issue Date: 2021
Publisher: Universidad de Extremadura, Servicio de Publicaciones
Abstract: 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 he q-cobrant objects (all objects are q-brant). As an application, we provide a new proof of the fact that the categorization functor from multipointed d-spaces to ows 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.
ISSN: 0213-8743
DOI: 10.17398/2605-5686.36.2.157
Appears in Collections:Extracta Mathematicae Vol. 36, nº 2 (2021)

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