LEADER 04750nam 2200613 450 001 9910481049903321 005 20170822144305.0 010 $a1-4704-0273-4 035 $a(CKB)3360000000464866 035 $a(EBL)3114568 035 $a(SSID)ssj0000889173 035 $a(PQKBManifestationID)11483297 035 $a(PQKBTitleCode)TC0000889173 035 $a(PQKBWorkID)10875643 035 $a(PQKB)11431328 035 $a(MiAaPQ)EBC3114568 035 $a(PPN)195415663 035 $a(EXLCZ)993360000000464866 100 $a19990928h20002000 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRational homotopical models and uniqueness /$fMartin Majewski 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2000] 210 4$dİ2000 215 $a1 online resource (175 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 682 300 $a"January 2000, volume 143, number 682 (end of volume)." 311 $a0-8218-1920-8 320 $aIncludes bibliographical references (pages 147-149). 327 $a""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. a??? as comonoids over the derived category""; ""2. Derived tensor product""; ""3. Generalizations""; ""A. EXAMPLES OF HOMOTOPICAL CATEGORIES"" 327 $a""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"" 327 $a""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 PBWa???Theorem""; ""3. Normal complete Hopf algebras"" 327 $a""4. Rigidity""""3. COMPLETE GROUPS""; ""1. Nilpotent groups""; ""2. Complete groups""; ""3. The Lazard a??? 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 a??? chain functor and the chain a??? loop functor"" 327 $a""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 a??? loop functor""; ""4. The group algebra of a free simplicial group""; ""5. A proof of the Quillen equivalence"" 327 $a""4. MAIN RESULTS"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 682. 606 $aHomotopy theory 606 $aHopf algebras 608 $aElectronic books. 615 0$aHomotopy theory. 615 0$aHopf algebras. 676 $a510 s 676 $a514/.24 700 $aMajewski$b Martin$f1963-$0962632 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910481049903321 996 $aRational homotopical models and uniqueness$92182799 997 $aUNINA