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L&S Cat Theory:
Attempted solutions to "Conceptual Mathematics" by Lawvere and Schanuel
Ryan Ruff
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Front Matter
1
Introduction
1.1
What is this?
1.2
Session 1
2
Part 1: The Category of Sets
2.1
Article 1: Sets, maps, composition
2.2
Session 2
2.3
Session 3
3
Part 2: The Algebra of Composition
3.1
Article 2: Isomorphisms, Part 1
3.2
Article 2: Isomorphisms, Part 2
3.3
Article 2: Isomorphisms, Part 3
3.4
Session 4: Division of maps: Isomorphisms
3.5
Session 5: Division of maps: Sections and retractions
3.6
Session 6: Two general aspects or uses of maps
3.7
Session 7: Isomorphisms and coordinates
3.8
Session 8: Pictures of a map
3.9
Session 9: Retracts and idempotents
3.10
Quiz
3.11
Summary/Quiz on Opposed Maps
3.12
Session 10: Brouwer’s theorems
4
Part 3: Categories of Structured Sets
4.1
Article 3: Examples of Categories, Part 1
4.2
Article 3: Examples of Categories, Part 2
4.3
Article 3: Examples of Categories, Part 3
4.4
Article 3: Examples of Categories, Part 4
4.5
Article 3: Examples of Categories, Part 5
4.6
Session 11: Ascending to categories of richer structures
4.7
Session 12: Categories of Diagrams
4.8
Session 13: Monoids
4.9
Session 14: Maps preserve positive properties
4.10
Session 15: Objectification of Properties
4.11
Session 15: Objectification of Properties, Part 2
4.12
Session 15: Objectification of Properties, Part 3
4.13
Session 15: Objectification of Properties, Part 4
4.14
Session 15: Objectification of Properties, Part 5
4.15
Session 15: Objectification of Properties, Part 6
4.16
Session 15: Objectification of Properties, Part 7
4.17
Session 16: Idempotents, involutions, and graphs
4.18
Session 17: Some uses of graphs
4.19
Session 18: Review of Test 2
5
Part 4: Elementary Universal Mapping Properties
5.1
Article 4: Universal Mapping Properties
5.2
Article 4: Universal Mapping Properties, Part 2
5.3
Article 4: Universal Mapping Properties, Part 3
5.4
Article 4: Universal Mapping Properties, Part 4
5.5
Article 4: Universal Mapping Properties, Part 5
5.6
Article 4: Universal Mapping Properties, Part 6
5.7
Article 4: Universal Mapping Properties, Part 7
5.8
Article 4: Universal Mapping Properties, Part 8
5.9
Article 4: Universal Mapping Properties, Part 9
5.10
Session 19: Terminal objects
5.11
Session 20: Points of an object
5.12
Session 21: Products in categories
5.13
Session 21: Products in categories, Part 2
5.14
Session 22: Universal mapping properties, Incidence Relations
5.15
Session 22: Universal mapping properties, Incidence Relations, Part 2
5.16
Session 22: Universal mapping properties, Incidence Relations, Part 3
5.17
Session 23: More on universal mapping properties
5.18
Session 23: More on universal mapping properties, Part 2
5.19
Session 23: More on universal mapping properties, Part 3
5.20
Session 23: More on universal mapping properties, Part 4
5.21
Session 24: Uniqueness of products and definition of sum
5.22
Session 24: Uniqueness of products and definition of sum, Part 2
5.23
Session 25: Labelings and products of graphs
5.24
Session 25: Labelings and products of graphs, Part 2
5.25
Revisiting Session 17, Part 1
5.26
Session 25: Labelings and products of graphs, Part 3
5.27
Session 25: Labelings and products of graphs, Part 4
5.28
Session 25: Labelings and products of graphs, Part 5
5.29
Session 25: Labelings and products of graphs, Part 6
5.30
Session 26: Distributive categories and linear categories
5.31
Session 26: Distributive categories and linear categories, Part 2
5.32
Session 26: Distributive categories and linear categories, Part 3
5.33
Session 27: Examples of universal constructions
5.34
Session 27: Examples of universal constructions, Part 2
5.35
Session 27: Examples of universal constructions, Part 3
5.36
Session 27: Examples of universal constructions, Part 4
5.37
Session 27: Examples of universal constructions, Part 5
5.38
Session 27: Examples of universal constructions, Part 6
5.39
Session 27: Examples of universal constructions, Part 7
5.40
Session 27: Examples of universal constructions, Part 8
5.41
Session 27: Examples of universal constructions, Part 9
5.42
Session 27: Examples of universal constructions, Part 10
5.43
Session 27: Examples of universal constructions, Part 11
5.44
Session 27: Examples of universal constructions, Part 12
5.45
Session 27: Examples of universal constructions, Part 13
Backmatter
Colophon
Colophon
This book was authored in PreTeXt.
