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Rational homotopical models and uniqueness / / Martin Majewski
| Rational homotopical models and uniqueness / / Martin Majewski |
| Autore | Majewski Martin <1963-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (175 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy theory
Hopf algebras |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0273-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. � 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 PBW�Theorem""; ""3. Normal complete Hopf algebras"" ""4. Rigidity""""3. COMPLETE GROUPS""; ""1. Nilpotent groups""; ""2. Complete groups""; ""3. The Lazard � 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 � chain functor and the chain � 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 � loop functor""; ""4. The group algebra of a free simplicial group""; ""5. A proof of the Quillen equivalence"" ""4. MAIN RESULTS"" |
| Record Nr. | UNINA-9910481049903321 |
Majewski Martin <1963->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Rational homotopical models and uniqueness / / Martin Majewski
| Rational homotopical models and uniqueness / / Martin Majewski |
| Autore | Majewski Martin <1963-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (175 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy theory
Hopf algebras |
| ISBN | 1-4704-0273-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. � 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 PBW�Theorem""; ""3. Normal complete Hopf algebras"" ""4. Rigidity""""3. COMPLETE GROUPS""; ""1. Nilpotent groups""; ""2. Complete groups""; ""3. The Lazard � 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 � chain functor and the chain � 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 � loop functor""; ""4. The group algebra of a free simplicial group""; ""5. A proof of the Quillen equivalence"" ""4. MAIN RESULTS"" |
| Record Nr. | UNINA-9910788739503321 |
|
Majewski Martin <1963->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Rational homotopical models and uniqueness / / Martin Majewski
| Rational homotopical models and uniqueness / / Martin Majewski |
| Autore | Majewski Martin <1963-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (175 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy theory
Hopf algebras |
| ISBN | 1-4704-0273-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. � 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 PBW�Theorem""; ""3. Normal complete Hopf algebras"" ""4. Rigidity""""3. COMPLETE GROUPS""; ""1. Nilpotent groups""; ""2. Complete groups""; ""3. The Lazard � 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 � chain functor and the chain � 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 � loop functor""; ""4. The group algebra of a free simplicial group""; ""5. A proof of the Quillen equivalence"" ""4. MAIN RESULTS"" |
| Record Nr. | UNINA-9910812747003321 |
|
Majewski Martin <1963->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||