close
1.

図書

図書
Steve Awodey
出版情報: Oxford ; New York : Oxford University Press, 2010  xv, 311 p. ; 24 cm
シリーズ名: Oxford logic guides ; 52
所蔵情報: loading…
目次情報: 続きを見る
Preface to the second edition
Preface
Categories / 1:
Introduction / 1.1:
Functions of sets / 1.2:
Definition of a category / 1.3:
Examples of categories / 1.4:
Isomorphisms / 1.5:
Constructions on categories / 1.6:
Free categories / 1.7:
Foundations: large, small, and locally small / 1.8:
Exercises / 1.9:
Abstract structures / 2:
Epis and monos / 2.1:
Initial and terminal objects / 2.2:
Generalized elements / 2.3:
Products / 2.4:
Examples of products / 2.5:
Categories with products / 2.6:
Hom-sets / 2.7:
Duality / 2.8:
The duality principle / 3.1:
Coproducts / 3.2:
Equalizers / 3.3:
Coequalizers / 3.4:
Groups and categories / 3.5:
Groups in a category / 4.1:
The category of groups / 4.2:
Groups as categories / 4.3:
Finitely presented categories / 4.4:
Limits and colimits / 4.5:
Subobjects / 5.1:
Pullbacks / 5.2:
Properties of pullbacks / 5.3:
Limits / 5.4:
Preservation of limits / 5.5:
Colimits / 5.6:
Exponentials / 5.7:
Exponential in a category / 6.1:
Cartesian closed categories / 6.2:
Heyting algebras / 6.3:
Propositional calculus / 6.4:
Equational definition of CCC / 6.5:
?-calculus / 6.6:
Variable sets / 6.7:
Naturality / 6.8:
Category of categories / 7.1:
Representable structure / 7.2:
Stone duality / 7.3:
Examples of natural transformations / 7.4:
Exponentials of categories / 7.6:
Functor categories / 7.7:
Monoidal categories / 7.8:
Equivalence of categories / 7.9:
Examples of equivalence / 7.10:
Categories of diagrams / 7.11:
Set-valued functor categories / 8.1:
The Yoneda embedding / 8.2:
The Yoneda lemma / 8.3:
Applications of the Yoneda lemma / 8.4:
Limits in categories of diagrams / 8.5:
Colimits in categories of diagrams / 8.6:
Exponentials in categories of diagrams / 8.7:
Topoi / 8.8:
Adjoints / 8.9:
Preliminary definition / 9.1:
Hom-set Definition / 9.2:
Examples of adjoints / 9.3:
Order adjoints / 9.4:
Quantifiers as adjoints / 9.5:
RAPL / 9.6:
Locally cartesian closed categories / 9.7:
Adjoint functor theorem / 9.8:
Monads and algebras / 9.9:
The triangle identities / 10.1:
Monads and adjoints / 10.2:
Algebras for a monad / 10.3:
Comonads and coalgebras / 10.4:
Algebras for endofunctors / 10.5:
Solutions to selected exercises / 10.6:
References
Index
Hom-set definition
Preface to the second edition
Preface
Categories / 1:
2.

図書

図書
J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F.W. Lawvere
出版情報: New York : Cambridge University Press, 2011  xvii, 249 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 184
所蔵情報: loading…
目次情報: 続きを見る
Foreword / F. W. Lawvere
Preface
Abstract Algebraic Categories / Part I:
Preliminaries / 0:
Algebraic theories and algebraic categories / 1:
Sifted and filtered colimits / 2:
Reflexive coequalizers / 3:
Algebraic categories as free completions / 4:
Properties of algebras / 5:
A characterization of algebraic categories / 6:
From filtered to sifted / 7:
Canonical theories / 8:
Algebraic functors / 9:
Birkhoff's variety theorem / 10:
Concrete Algebraic Categories / Part II:
One-sorted algebraic categories / 11:
Algebras for an endofunctor / 12:
Equational categories of ?-algebras / 13:
S-sorted algebraic categories / 14:
Special Topics / Part III:
Morita equivalence / 15:
Free exact categories / 16:
Exact completion and reflexive-coequalizer completion / 17:
Finitary localizations of algebraic categories / 18:
Postscript
Monads / Appendix A:
Abelian categories / Appendix B:
More about dualities for one-sorted algebraic categories / Appendix C:
References
List of symbols
Index
Foreword / F. W. Lawvere
Preface
Abstract Algebraic Categories / Part I:
3.

図書

図書
Saunders Mac Lane
出版情報: New York : Springer, c1998  xii, 314 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 5
所蔵情報: loading…
4.

図書

図書
Masaki Kashiwara, Pierre Schapira
出版情報: Berlin ; New York : Springer, c2006  x, 497 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; v. 332
所蔵情報: loading…
目次情報: 続きを見る
Introduction
The Language of Categories / 1:
Preliminaries: Sets and Universes / 1.1:
Categories and Functors / 1.2:
Morphisms of Functors / 1.3:
The Yoneda Lemma / 1.4:
Adjoint Functors / 1.5:
Exercises
Limits / 2:
Examples / 2.1:
Kan Extension of Functors / 2.3:
Inductive Limits in the Category Set / 2.4:
Cofinal Functors / 2.5:
Ind-lim and Pro-lim / 2.6:
Yoneda Extension of Functors / 2.7:
Filtrant Limits / 3:
Filtrant Inductive Limits in the Category Set / 3.1:
Filtrant Categories / 3.2:
Exact Functors / 3.3:
Categories Associated with Two Functors / 3.4:
Tensor Categories / 4:
Projectors / 4.1:
Rings, Modules and Monads / 4.2:
Generators and Representability / 5:
Strict Morphisms / 5.1:
Strictly Generating Subcategories / 5.2:
Indization of Categories / 6:
Indization of Categories and Functors / 6.1:
Representable Ind-limits / 6.2:
Indization of Categories Admitting Inductive Limits / 6.3:
Finite Diagrams in Ind(C) / 6.4:
Localization / 7:
Localization of Categories / 7.1:
Localization of Subcategories / 7.2:
Localization of Functors / 7.3:
Indization and Localization / 7.4:
Additive and Abelian Categories / 8:
Group Objects / 8.1:
Additive Categories / 8.2:
Abelian Categories / 8.3:
Injective Objects / 8.4:
Ring Action / 8.5:
Indization of Abelian Categories / 8.6:
Extension of Exact Functors / 8.7:
[pi]-accessible Objects and F-injective Objects / 9:
Cardinals / 9.1:
[pi]-filtrant Categories and [pi]-accessible Objects / 9.2:
[pi]-accessible Objects and Generators / 9.3:
Quasi-Terminal Objects / 9.4:
F-injective Objects / 9.5:
Applications to Abelian Categories / 9.6:
Triangulated Categories / 10:
Localization of Triangulated Categories / 10.1:
Localization of Triangulated Functors / 10.3:
Extension of Cohomological Functors / 10.4:
The Brown Representability Theorem / 10.5:
Complexes in Additive Categories / 11:
Differential Objects and Mapping Cones / 11.1:
The Homotopy Category / 11.2:
Simplicial Constructions / 11.3:
Double Complexes / 11.5:
Bifunctors / 11.6:
The Complex Hom / 11.7:
Complexes in Abelian Categories / 12:
The Snake Lemma / 12.1:
Abelian Categories with Translation / 12.2:
Example: Koszul Complexes / 12.3:
Derived Categories / 12.5:
Resolutions / 13.1:
Derived Functors / 13.3:
Unbounded Derived Categories / 13.4:
Derived Categories of Abelian Categories with Translation / 14.1:
Unbounded Derived Category / 14.2:
Left Derived Functors / 14.4:
Indization and Derivation of Abelian Categories / 15:
Injective Objects in Ind(C) / 15.1:
Quasi-injective Objects / 15.2:
Derivation of Ind-categories / 15.3:
Indization and Derivation / 15.4:
Grothendieck Topologies / 16:
Sieves and Local Epimorphisms / 16.1:
Local Isomorphisms / 16.2:
Localization by Local Isomorphisms / 16.3:
Sheaves on Grothendieck Topologies / 17:
Presites and Presheaves / 17.1:
Sites / 17.2:
Sheaves / 17.3:
Sheaf Associated with a Presheaf / 17.4:
Direct and Inverse Images / 17.5:
Restriction and Extension of Sheaves / 17.6:
Internal Hom / 17.7:
Abelian Sheaves / 18:
R-modules / 18.1:
Tensor Product and Internal Hom / 18.2:
Derived Functors for Hom and Hom / 18.3:
Flatness / 18.5:
Ringed Sites / 18.6:
Cech Coverings / 18.7:
Stacks and Twisted Sheaves / 19:
Prestacks / 19.1:
Simply Connected Categories / 19.2:
Stacks / 19.3:
Morita Equivalence / 19.5:
Twisted Sheaves / 19.6:
References
List of Notations
Index
Introduction
The Language of Categories / 1:
Preliminaries: Sets and Universes / 1.1:
5.

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
所蔵情報: loading…
6.

図書

図書
A.J. Berrick, M.E. Keating
出版情報: Cambridge : Cambridge University Press, 2000  xvii, 361 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 67
所蔵情報: loading…
目次情報: 続きを見る
Categories / 1:
Categories and exact sequences / 2:
Change of rings / 3:
The Morita theory / 4:
Limits in categories / 5:
Localisation / 6:
Local-global methods / 7:
Categories / 1:
Categories and exact sequences / 2:
Change of rings / 3:
7.

図書

図書
by Amnon Neeman
出版情報: Princeton, N.J. : Princeton University Press, 2001  vii, 449 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 148
所蔵情報: loading…
8.

図書

図書
[edited by] Tom Leinster
出版情報: Cambridge : Cambridge University Press, 2004  xiii, 433 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 298
所蔵情報: loading…
目次情報: 続きを見る
Background / Part I:
Classical categorical structures / 1:
Classical operads and multicategories / 2:
Notions of monoidal category / 3:
Operads / Part II:
Generalized operads and multicategories: basics / 4:
Example: fc-multicategories / 5:
Generalized operads and multicategories: further theory / 6:
Opetopes / 7:
n-categories / Part III:
Globular operads / 8:
A definition of weak n-category / 9:
Other definitions of weak n-category / 10:
A Symmetric structures / Appendices:
Coherence for monoidal categories / B:
Special Cartesian monads / C:
Free multicategories / D:
Definitions of trees / E:
Free strict n-categories / F:
Initial operad-with-contraction / G:
Background / Part I:
Classical categorical structures / 1:
Classical operads and multicategories / 2:
9.

図書

図書
H.R. Margolis
出版情報: Amsterdam ; New York : North-Holland , New York, NY : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1983  xix, 489 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 29
所蔵情報: loading…
10.

図書

図書
Dieter Happel
出版情報: Cambridge : Cambridge University Press, 1988  ix, 208 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 119
所蔵情報: loading…
目次情報: 続きを見る
Preface
Triangulated categories / 1:
Repetitive algebras / 2:
Tilting theory / 3:
Piecewise hereditary algebras / 4:
Trivial extension algebras / 5:
References
Index
Preface
Triangulated categories / 1:
Repetitive algebras / 2:
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼