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1.

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
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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:
2.

図書

図書
Jiří Adámek, Horst Herrlich, George E. Strecker
出版情報: New York : Wiley, c1990  xii, 482 p. ; 26 cm
シリーズ名: Pure and applied mathematics
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Motivation
Foundations
Categories, Functors, And Natural Transformations
Categories and Functors
Subcategories
Concrete Categories and Concrete Functors
Natural Transformations
Objects And Morphisms
Objects and Morphisms in Abstract Categories
Objects and Morphisms in Concrete Categories
Injective Objects and Essential Embeddings
Sources And Sinks
Sources and Sinks
Limits and Colimits
Completeness and Cocompleteness
Functors and Limits
Factorization Structures
Factorization Structures for Morphisms
Factorization Structures for Sources
E-Reflective Subcategories
Factorization Structures for Functors
Adjoints And Monads
Adjoint Functors
Adjoint Situations
Monads
Topological And Algebraic Categories
Topological Categories
Topological Structure Theorems
Algebraic Categories
Algebraic Structure Theorems
Topologically Algebraic Categories
Topologically Algebraic Structure Theorems
Cartesian Closedness And Partial Morphisms
Cartesian Closed Categories
Partial Morphisms, Quasitopoi, and Topological Universes
Bibliography
Tables
Table of Categories
Table of Symbols
Index
Motivation
Foundations
Categories, Functors, And Natural Transformations
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