Modules over operads and functors / Benoit Fresse
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1967Langue : anglais.Éditeur : Berlin : Springer, 2009ISBN: 9783540890553.ISSN: 1617-9692.Sujet MSC : 18M60, Monoidal categories and operads, Operads (general)55P48, Algebraic topology - Homotopy theory, Loop space machines and operads
18N40, Higher categories and homotopical algebra, Homotopical algebra, Quillen model categories, derivators
18A25, General theory of categories and functors, Functor categories, comma categories
18-02, Research exposition (monographs, survey articles) pertaining to category theoryEn-ligne : Springerlink | Zentralblatt | MathSciNet
This book gives a very useful categorical, homotopical and operadic background.
Introduced in order to model structure of iterated loop spaces, operads have been used fruitfully in many fields of mathematics and physic.
The main purpose of this monograph is to study modules over operads (which occure naturally in many frameworks) as a device to model functors between categories of algebras as effectively as operads model categories of algebras.
A first result, and the motivation of this work, says that functors determinated by modules over operads satisfy good homotopy invariance properties. (Zentralblatt)
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