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1.

図書

図書
Mark Hovey
出版情報: Providence, R.I. : American Mathematical Society, c1999  xii, 209 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 63
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目次情報: 続きを見る
Preface
Model categories / Chapter 1.:
The definition of a model category / 1.1.:
The homotopy category / 1.2.:
Quillen functors and derived functors / 1.3.:
Quillen functors / 1.3.1.:
Derived functors and naturality / 1.3.2.:
Quillen equivalences / 1.3.3.:
2-categories and pseudo-2-functors / 1.4.:
Examples / Chapter 2.:
Cofibrantly generated model categories / 2.1.:
Ordinals, cardinals, and transfinite compositions / 2.1.1.:
Relative I-cell complexes and the small object argument / 2.1.2.:
The stable category of modules / 2.1.3.:
Chain complexes of modules over a ring / 2.3.:
Topological spaces / 2.4.:
Chain complexes of comodules over a Hopf algebra / 2.5.:
The category of B-comodules / 2.5.1.:
Weak equivalences / 2.5.2.:
The model structure / 2.5.3.:
Simplicial sets / Chapter 3.:
The model structure on simplicial sets / 3.1.:
Anodyne extensions / 3.3.:
Homotopy groups / 3.4.:
Minimal fibrations / 3.5.:
Fibrations and geometric realization / 3.6.:
Monoidal model categories / Chapter 4.:
Closed monoidal categories and closed modules / 4.1.:
Monoidal model categories and modules over them / 4.2.:
The homotopy category of a monoidal model category / 4.3.:
Framings / Chapter 5.:
Diagram categories / 5.1.:
Diagrams over Reedy categories and framings / 5.2.:
A lemma about bisimplicial sets / 5.3.:
Function complexes / 5.4.:
Associativity / 5.5.:
Naturality / 5.6.:
Framings on pointed model categories / 5.7.:
Pointed model categories / Chapter 6.:
The suspension and loop functors / 6.1.:
Cofiber and fiber sequences / 6.2.:
Properties of cofiber and fiber sequences / 6.3.:
Naturality of cofiber sequences / 6.4.:
Pre-triangulated categories / 6.5.:
Pointed monoidal model categories / 6.6.:
Stable model categories and triangulated categories / Chapter 7.:
Triangulated categories / 7.1.:
Stable homotopy categories / 7.2.:
Weak generators / 7.3.:
Finitely generated model categories / 7.4.:
Vistas / Chapter 8.:
Bibliography
Index
Preface
Model categories / Chapter 1.:
The definition of a model category / 1.1.:
2.

図書

図書
J. R. García Rozas
出版情報: Boca Raton : Chapman & Hall/CRC Press, c1999  137 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 407
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3.

図書

図書
by C.M. Jessop
出版情報: New York : Chelsea Pub. Co, [1969]  xv, 364 p ; 21 cm
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4.

図書

図書
by Nikolai N. Tarkhanov
出版情報: Dordrecht [Nehterlands] : Kluwer Academic Publishers, c1995  xviii, 396 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 340
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5.

図書

図書
Bruce Hughes, Andrew Ranicki
出版情報: New York : Cambridge University Press, 1996  xxv, 353 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 123
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目次情報: 続きを見る
Topology at infinity / 1:
Topology over the real line / 2:
The algebraic theory / 3:
Appendices
Topology at infinity / 1:
Topology over the real line / 2:
The algebraic theory / 3:
6.

図書

図書
David Anick
出版情報: Wellesley, Mass. : A.K. Peters, c1993  xxv, 274 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 3
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7.

図書

図書
by J. Peter May
出版情報: Chicago ; London : University of Chicago Press, 1992  viii, 161 p. ; 22 cm
シリーズ名: Chicago lectures in mathematics
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目次情報: 続きを見る
Simplicial Objects and Homotopy / I:
Definitions and examples / 1:
Simplicial objects in categories; homology / 2:
Homotopy of Kan complexes / 3:
The group structures / 4:
Homotopy of simplicial maps / 5:
Function complexes / 6:
Bibliographical notes on chapter I
Fibrations, Postnikov Systems, and Minimal Complexes / II:
Kan fibrations / 7:
Postnikov systems / 8:
Minimal complexes / 9:
Minimal fibrations / 10:
Fibre products and fibre bundles / 11:
Weak homotopy type / 12:
The Hurewicz theorems / 13:
Bibliographical notes on chapter II
Geometric Realization / III:
The realization / 14:
Adjoint functors / 15:
Comparison of simplicial sets and topological spacesBibliographical notes on chapter III / 16:
Twisted Cartesian Products and Fibre Bundles / IV:
Simplicial groups / 17:
Principal fibrations and twisted Cartesian products / 18:
The group of a fibre bundle / 19:
Fibre bundles and twisted Cartesian products / 20:
Universal bundles and classifying complexes / 21:
Bibliographical notes on chapter IV
Eilenberg-Maclane Complexes and Postnikov Systems / V:
Simplicial Abelian groups / 22:
Eilenberg-MacLane complexes / 23:
K(rr, n)'s and cohomology operations / 24:
The k-invariants of Postnikov systems / 25:
Bibliographical notes on chapter V
Loop Groups, Acyclic Models, and Twisted Tensor Products / VI:
Loop groups / 26:
The functors G, W, and E / 27:
Acyclic models / 28:
The Eilenberg-Zilber theorem / 29:
Cup, Pontryagin, and cap products; twisting cochains / 30:
Brown's theorem / 31:
The Serre spectral sequence / 32:
Bibliographical notes on chapter VI
Bibliography
Simplicial Objects and Homotopy / I:
Definitions and examples / 1:
Simplicial objects in categories; homology / 2:
8.

図書

図書
Myles Tierney
出版情報: Berlin ; New York : Springer-Verlag, 1969  65 p. ; 28 cm
シリーズ名: Lecture notes in mathematics ; 87
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9.

図書

図書
Rudolph Fritsch, Renzo A. Piccinini
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1990  xi, 326 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 19
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目次情報: 続きを見る
The fundamental properties of CW-complexes / 1:
Categories of CW-complexes / 2:
Polyhedra and simplicial complexes / 3:
Simplicial sets / 4:
Spaces of the homotopy type of a CW-complex / 5:
Appendixes
The fundamental properties of CW-complexes / 1:
Categories of CW-complexes / 2:
Polyhedra and simplicial complexes / 3:
10.

図書

図書
Kentaro Yano
出版情報: Oxford : Pergamon Press, 1965  xii, 326 p. ; 23 cm
シリーズ名: International series of monographs on pure and applied mathematics ; v. 49
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