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Abstract and concrete categories

By: Contributor(s): Material type: TextTextLanguage: English Series: Pure and applied mathematicsPublication details: New York John Wiley & Sons 1990Description: xii, 482p. illISBN:
  • 041609226 (HB)
Subject(s):
Contents:
0.Introduction 1. Motivation 2. Foundations, I. Categories, Functors, and Natural Transformations 3. Categories and Functors 4. Subcategories 5. Concrete Categories and Concrete Functors 6. Natural Transformations II. Objects and Morphisms 7. Objects and Morphisms in Abstract Categories 8. Objects and Morphisms in Concrete Categories 9. Injective Objects and Essential Embeddings III. Sources and Sinks 10. Sources and Sinks 11. Limits and Colimits 12. Completeness and Cocompleteness 13. Functors and Limits IV. Factorization Structures 14. Factorization Structures for Morphisms 15. Factorization Structures for Sources 16. E-Reflective Subcategories 17. Factorization Structures for Functors V. Adjoints and Monads 18. Adjoint Functors 19. Adjoint Situations 20. Monads VI. Topological and Algebraic Categories 21. Topological Categories 22. Topological Structure Theorems 23. Algebraic Categories 24. Algebraic Structure Theorems 25. Topologically Algebraic Categories 26. Topologically Algebraic Structure Theorems VII. Cartesian Closedness and Partial Morphisms 27. Cartesian Closed Categories 28. Partial Morphisms, Quasitopoi, and Topological Universes Monads VI. Topological and Algebraic Categories Topological Categories Topological Structure Theorems Algebraic Categories Algebraic Structure Theorems Topologically Algebraic Categories Topologically Algebraic Structure Theorems VII. Cartesian Closedness and Partial Morphisms Cartesian Closed Categories Partial Morphisms, Quasitopoi, and Topological Universes
Summary: The theory of structure is introduced via the language of category theory in this text, which focuses on concrete categories. The authors also provide a systematic treatment of factorization structures, which gives a unifying perspective to past work and summarizes recent developments.
Item type: BOOKS
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IMSc Library 512.58 ADA (Browse shelf(Opens below)) Available 29117

Includes index

Includes bibliographical references

0.Introduction
1. Motivation
2. Foundations,
I. Categories, Functors, and Natural Transformations
3. Categories and Functors
4. Subcategories
5. Concrete Categories and Concrete Functors
6. Natural Transformations
II. Objects and Morphisms
7. Objects and Morphisms in Abstract Categories
8. Objects and Morphisms in Concrete Categories
9. Injective Objects and Essential Embeddings
III. Sources and Sinks
10. Sources and Sinks
11. Limits and Colimits
12. Completeness and Cocompleteness
13. Functors and Limits
IV. Factorization Structures
14. Factorization Structures for Morphisms
15. Factorization Structures for Sources
16. E-Reflective Subcategories
17. Factorization Structures for Functors
V. Adjoints and Monads
18. Adjoint Functors
19. Adjoint Situations
20. Monads
VI. Topological and Algebraic Categories
21. Topological Categories
22. Topological Structure Theorems
23. Algebraic Categories
24. Algebraic Structure Theorems
25. Topologically Algebraic Categories
26. Topologically Algebraic Structure Theorems
VII. Cartesian Closedness and Partial Morphisms
27. Cartesian Closed Categories
28. Partial Morphisms, Quasitopoi, and Topological Universes

Monads

VI. Topological and Algebraic Categories

Topological Categories

Topological Structure Theorems

Algebraic Categories

Algebraic Structure Theorems

Topologically Algebraic Categories

Topologically Algebraic Structure Theorems

VII. Cartesian Closedness and Partial Morphisms
Cartesian Closed Categories
Partial Morphisms, Quasitopoi, and Topological Universes

The theory of structure is introduced via the language of category theory in this text, which focuses on concrete categories. The authors also provide a systematic treatment of factorization structures, which gives a unifying perspective to past work and summarizes recent developments.

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The Institute of Mathematical Sciences, Chennai, India