000			04935nam a22004693i 4500
001			EBC3114568
003			MiAaPQ
005			20240729124612.0
006			m o d |
007			cr cnu||||||||
008			240724s1999 xx o ||||0 eng d
020			_a9781470402730 _q(electronic bk.)
020			_z9780821819203
035			_a(MiAaPQ)EBC3114568
035			_a(Au-PeEL)EBL3114568
035			_a(CaPaEBR)ebr11041346
035			_a(OCoLC)922965062
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA612.7 -- .M35 2000eb
082	0		_a510 s;514/.24
100	1		_aMajewski, Martin.
245	1	0	_aRational Homotopical Models and Uniqueness.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c1999.
264		4	_c©2000.
300			_a1 online resource (175 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.143
505	0		_aIntro -- 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.
505	8		_a1. 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 -- 1. Summary -- 2. Anick's equivalence -- 3. Proof of the Baues - Lemaire conjecture -- 4. Rational equivalence -- D. THE CELLULAR LIE ALGEBRA MODEL -- 1. A natural diagonal for the cobar - chain functor -- 2. A natural Hopf diagonal -- 3. The category of dg Lie algebras (over any ring) -- 4. Anick's theorems and naturality -- NOTATIONS -- BIBLIOGRAPHY.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aHomotopy theory.
650		0	_aHopf algebras.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aMajewski, Martin _tRational Homotopical Models and Uniqueness _dProvidence : American Mathematical Society,c1999 _z9780821819203
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114568 _zClick to View
999			_c70063 _d70063