Rational homotopical models and uniqueness / / Martin Majewski

• Autore: Majewski Martin <1963->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2000]; ©2000
• Descrizione fisica: 1 online resource (175 p.)
• Disciplina: 510 s; 514/.24
• Soggetto topico: Homotopy theory; Hopf algebras
• Note generali: "January 2000, volume 143, number 682 (end of volume)."
• Nota di bibliografia: Includes bibliographical references (pages 147-149).
• Nota di contenuto: ""TABLE OF CONTENTS""; ""ABSTRACT""; ""KEYWORDS""; ""PREFACE""; ""INTRODUCTION""; ""1. HOMOTOPY THEORY""; ""1. HOMOTOPICAL CATEGORIES""; ""1. The axioms""; ""2. Left homotopical categories""; ""3. Homotopical subcategories""; ""2. FUNDAMENTAL RESULTS""; ""1. Lifting and extension""; ""2. The derived category""; ""3. Homotopical functors and their derived functors""; ""4. The Adjoint Functor Theorem""; ""3. COMONOIDS UP TO HOMOTOPY""; ""1. â€? as comonoids over the derived category""; ""2. Derived tensor product""; ""3. Generalizations""; ""A. EXAMPLES OF HOMOTOPICAL CATEGORIES"" ; ""1. Cofibration categories""""2. Model categories""; ""3. Spaces""; ""4. Simplicial objects""; ""2. DIFFERENTIAL ALGEBRA""; ""1. PRELIMINARIES""; ""1. Chain complexes""; ""2. DG (co)algebras""; ""3. Tensor (co) algebras""; ""2. TWISTING MAPS AND THE (CO) BAR CONSTRUCTION""; ""1. Twisting maps and homotopies""; ""2. The (co)bar construction""; ""3. Compatibility with tensor product""; ""4. Homological properties""; ""3. ACYCLIC MODELS""; ""1. Representable functors""; ""2. The method of acyclic models""; ""3. Duality""; ""4. Acyclic model theorems for twisting maps""; ""4. EZ-MORPHISMS"" ; ""1. Extension of an EZ-morphism""""2. A generalization""; ""3. Properties of the extension""; ""B. CHAIN (CO) FUNCTORS""; ""1. Monoidal categories""; ""2. Normalization""; ""3. Representable cofunctors for spaces""; ""4. Cohomology theories""; ""3. COMPLETE ALGEBRA""; ""1. COMPLETE AUGMENTED ALGEBRAS""; ""1. Ring systems""; ""2. Complete modules""; ""3. Complete augmented algebras and free groups""; ""4. Rigidity""; ""2. COMPLETE LIE ALGEBRAS AND COMPLETE HOPF ALGEBRAS""; ""1. Complete Hopf algebras and the exponential mapping""; ""2. The PBWâ€?Theorem""; ""3. Normal complete Hopf algebras"" ; ""4. Rigidity""""3. COMPLETE GROUPS""; ""1. Nilpotent groups""; ""2. Complete groups""; ""3. The Lazard â€? Mal'cev correspondence""; ""4. The Quillen functor""; ""C. FILTERED MODULES""; ""1. Filtered vs. cofiltered modules""; ""2. Normal maps and exactness""; ""3. Filtered tensor product""; ""4. Complete Differential Algebra""; ""4. THREE MODELS FOR SPACES""; ""1. THE CELLULAR MODEL""; ""1. The homotopical category of dg algebras""; ""2. The homotopical category of dg Hopf algebras up to homotopy""; ""3. The cobar â€? chain functor and the chain â€? loop functor"" ; ""4. Compatibility with (tensor) products""""5. The homotopy diagonals""; ""2. THE SULLIVAN MODEL""; ""1. The homotopical category of commutative dg* algebras""; ""2. The Sullivan cofunctor and Stokes' map""; ""3. Extension of Stokes' map""; ""4. Compatibility with (tensor) products""; ""5. Dualization""; ""6. The homotopy diagonals""; ""3. THE QUILLEN MODEL""; ""1. The homotopical category of dg Lie algebras""; ""2. The Quillen functor""; ""3. Connection to the chain â€? loop functor""; ""4. The group algebra of a free simplicial group""; ""5. A proof of the Quillen equivalence"" ; ""4. MAIN RESULTS""
• Titolo autorizzato: Rational homotopical models and uniqueness
• ISBN: 1-4704-0273-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910788739503321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; no. 682.