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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
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Abstract And Concrete Categories
The Joy of Cats
Jirl Adamek,
Horst Herrlich,
George E. Strecker
The Joy of Cats
Jirl Adamek,
Horst Herrlich,
George E. Strecker
Table of Contents
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
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