Goodwillie Approximations to Higher Categories - Couverture souple

Heuts, Gijs

 
9781470448936: Goodwillie Approximations to Higher Categories
Couverture souple
ISBN 10 : 1470448939 ISBN 13 : 9781470448936
Editeur : American Mathematical Society, 2022

Synopsis

We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More gen-erally, we construct such a tower for a large class of ?-categories C and classify such Goodwillie towers in terms of thederivatives of the identity functor of C.Asa particular application we show how this provides a model for the homotopy theory of simply-connected spaces in terms of coalgebras in spectra with Tate diagonals. Our classification of Goodwillie towers simplifies considerably in settings where the Tate cohomology of the symmetric groups vanishes. As an example we apply our methods to rational homotopy theory. Another application identifies the homotopy theory of p-local spaces with homotopy groups in a certain finite range with the homotopy theory of certain algebras over Ching's spectral version of the Lie operad. This is a close analogue of Quillen's results on rational homotopy.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Gijs Heuts, University of Copenhagen, Denmark.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2022
Langue
anglais
ISBN 10 
1470448939
ISBN 13 
9781470448936
Reliure
Broché
Nombre de pages
277
Coordonnées du fabricant
non disponible
Personne responsable
non disponible