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

Ducoulombier, Julien; Fresse, Benoit; Turchin, Victor

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s10485-022-09675-z

Title :

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

Author(s) :

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

Journal title :

Applied Categorical Structures

Pages :

825-920

Publisher :

Springer Verlag (Germany)

Publication date :

2022-04-08

ISSN :

0927-2852

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

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

Comment :

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

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