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http://hdl.handle.net/10662/12876
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. |
URI: | http://hdl.handle.net/10662/12876 |
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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2605-5686_36_2_157.pdf | 745,19 kB | Adobe PDF | View/Open |
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