Last edited by JoJojin
Tuesday, July 28, 2020 | History

3 edition of Modules over operads and functors found in the catalog.

# Modules over operads and functors

## by Benoit Fresse

Written in English

Subjects:
• Modules (Algebra),

• Edition Notes

Includes bibliographical references (p. 291-294) and index.

Classifications The Physical Object Statement Benoit Fresse Series Lecture notes in mathematics -- 1967 Contributions SpringerLink (Online service) LC Classifications QA247 .F67 2009 Pagination ix, 308 p. : Number of Pages 308 Open Library OL25543796M ISBN 10 3540890556, 3540890564 ISBN 10 9783540890553, 9783540890560 OCLC/WorldCa 269435377

6 CONTENTS 6 The Calculus of Functors The Calculus of Functors n-Excisive. The most completed version of this research has been published in the book of my publication list. The main original result of this book is a general homotopy invariance theorem which asserts that, under standard cofibration assumptions of homotopy theory, the functors associated to modules over operads preserve homotopy equivalences.

Modules over Operads and Functors. Find all books from Benoit Fresse. At io-holding.com you can find used, antique and new books, compare results and immediately purchase your selection at the best price. The notion of an operad supplies both a Brand: Springer-Verlag Gmbh. Sep 18,  · , Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: , page 35, In this chapter, we recall the definition of the category of ∗-objects and we review the relationship between ∗-objects and functors.

Homotopy theory of modules over operads and non-Σ operads in monoidal model categories. Author links open overlay panel John E. Harper. Show more. Modules Over Operads and Functors, Lecture Notes in Mathematics, vol. , Springer-Verlag, Berlin () Google Scholar An untitled book project about symmetric spectra, July, Cited by: We describe the multiplicative structures that arise on categories of equivariant modules over certain equivariant commutative ring spectra. Building on our previous work on N-infinity ring spectra, we construct categories of equivariant operadic modules over N-infinity rings that are structured by equivariant linear isometries operads.

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The purpose of this book is to obtain a similar relationship for functors on a category of algebras over an operad. We observe that right modules over operads, symmetric modules equipped with a right operad action, give rise to functors on categories of algebras and we prove that this construction yields an embedding of categories.

We observe that right modules over operads, symmetric modules equipped with a right operad action, give rise to functors on categories of algebras and we prove that this construction yields an embedding of categories. Then we check that right modules over operads form a model category. In addition we prove that weak-equivalences of.

Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

Homotopy of Algebras over Operads -- (Co)homology of Algebras over Operads -- Some Objectives for the Next Part -- Bibliographical Comments on Part III -- pt.

Homotopy of Modules over Operads and Functors -- Model Category of Right Modules over an Operad -- Modules and Homotopy Invariance of Functors -- The homotopy of algebras over operads.- The (co)homology of algebras over operads.- The homotopy of modules over operads and functors.- The model category of right modules.- Modules and homotopy invariance of functors.- Extension and restriction functors and model structures.- Miscellaneous applications.- Appendix: technical verifications.

The purpose of this book is to obtain a similar relationship for functors on a category of algebras over an operad. We observe that right modules over operads, symmetric modules equipped with a right operad action, give rise to functors on categories of algebras and we prove that this construction yields an embedding of io-holding.com by: We observe that right modules over operads, symmetric modules equipped with a right operad action, give rise to functors on categories of algebras and we prove that this construction yields an Author: Benoit Fresse.

Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of io-holding.com by: modules over operads as a device to model functors between categories of algebras as eﬀectively as operads model categories of algebras.

Modules over operads occur naturally when one needs to represent univer-sal complexes associated to algebras over operads (see [14, 54]).

Modules over operads have not been studied as extensively as operads yet. Modules Over Operads and Functors This monograph presents a review of the basis of operad theory.

It also studies structures of Modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras. Operads 9 2. Algebras over operads 11 3. Monadic reinterpretation of algebras 13 4. Modules over C-algebras 16 5.

Algebraic operads associated to topological operads 20 6. Operads, loop spaces, n-Lie algebras, and n-braid algebras 22 7. Homology operations in characteristic p 25 Part II.

Partial algebraic structures and conversion theorems 26 1. This monograph presents a review of the basis of operad theory. It also studies structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

Modules over Operads and FunctorsBrand: Textstream. nLab operad Skip the Navigation Links | Home Page The original definition is due to Peter May and was given in his book (The Geometry of Iterated Loop Spaces). It describes an operad as a collection of operations equipped with a notion of composition and subject to various conditions.

Benoit Fresse, Modules over operads and functors. The purpose of this book is to obtain a similar relationship for functors on a category of algebras over an operad. We observe that right modules over operads, symmetric modules equipped with a right operad action, give rise to functors on categories of algebras and we prove that this construction yields an embedding of io-holding.com: Benoit Fresse.

Jan 28,  · Part of the Lecture Notes in Mathematics book series (LNM, volume ) The purpose of Fresse B. () Shifted modules over operads and functors.

In: Modules over Operads and Functors. Lecture Notes in Mathematics, vol Springer, Berlin, Heidelberg. First Cited by: 1. OPERADS, ALGEBRAS, MODULES, AND MOTIVES IGOR KRIZ AND J.P.

MAY Submitted January 27, Contents Introduction 3 Part I. De nitions and examples of operads and operad actions 10 1. Operads 10 2. Algebras over operads 13 3. Monadic reinterpretation of algebras 16 4.

Modules over C-algebras 19 5. Algebraic operads associated to topological Cited by: This result is mentioned by Benoit Fresse in Modules over Operads and Functors, at the beginning of section The proof is based on the existence of a right adjoint $\Gamma\colon Endo(\mathrm{Vect}_k)\rightarrow\mathbb{S}\text{-}mod$.

Operads are a nice framework to model all kinds of different algebras, i.e. Monoids are algebras over the operad Assoc in the category of sets Associative algebras are algebras over the operad Ass.

[Show full abstract] relationship for functors on a category of algebras over an operad. We observe that right modules over operads, symmetric modules equipped with a right operad action, give Author: Vladimir Molotkov. History. Operads originate in algebraic topology from the study of iterated loop spaces by J.

Michael Boardman and Rainer M. Vogt, and J. Peter May. The word "operad" was created by May as a portmanteau of "operations" and "monad" (and also because his mother was an opera singer). Interest in operads was considerably renewed in the early 90s when, based on early insights of Maxim.

For (1), I recommend the paper Motivic Functors by Dundas-Rondigs-Ostvaer. They compare many different models for SH(k), with an eye towards monoidal properties (i.e.

pushout product axiom, monoid axiom, axiom that cofibrant objects are flat).If F and G is a pair of adjoint functors, then F C and G C is also a pair of adjoint functors.

The functor category D C has all the formal properties of an exponential object; in particular the functors from E × C → D stand in a natural one-to-one correspondence with the functors from E to D C.--Benoît Fresse's book "Modules over operads and functors" --Loday and Vallette's book on algebraic operads.

Also, there are videos of many lectures from the Newton Institute emphasis semester Grothendieck-Teichmüller groups, operads and deformation" or from MSRI that could be useful for preparing lectures in this series, as well as for.