Projective and Reedy model category structures for (infinitesimal) bimodules over an operad

Ducoulombier, Julien; Fresse, Benoit; Turchin, Victor

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s10485-022-09675-z

Titre :

Projective and Reedy model category structures for (infinitesimal) bimodules over an operad

Auteur(s) :

Ducoulombier, Julien [Auteur]
Fresse, Benoit [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Turchin, Victor [Auteur]
Department of Mathematics [University of Kansas]

Titre de la revue :

Applied Categorical Structures

Pagination :

825-920

Éditeur :

Springer Verlag (Germany)

Date de publication :

2022-04-08

ISSN :

0927-2852

Discipline(s) HAL :

Mathématiques [math]
Mathématiques [math]/Topologie algébrique [math.AT]

Résumé en anglais : [en]

We study projective and Reedy model category structures for bimodules and infinitesimal bimodules over a topological operad. In both cases, we build explicit cofibrant and fibrant replacements. We show that these categories ...
Lire la suite >We study projective and Reedy model category structures for bimodules and infinitesimal bimodules over a topological operad. In both cases, we build explicit cofibrant and fibrant replacements. We show that these categories are right proper and, under some conditions, left proper. We study the Extension/Restriction adjunctions. We give also a characterisation of Reedy cofibrations and we check that the two model structures produce compatible homotopy categories. In the case of bimodules the homotopy category induced by the Reedy model structure is a subcategory of the projective one. In the case of infinitesimal bimodules the Reedy and projective homotopy categories are the same.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Opérades, Calcul et méthodes de théorie de l'Homotopie en Topologie

Commentaire :

This paper is a preliminary version and we will appreciate all comments on this work

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