Category Theory: a concise course

• 1. Preface
• 2. Basic Definitions
  • 2.1. A motivating example
  • 2.2. Definition of a category
  • 2.3. Philosophy of category theory
  • 2.4. Solutions
• 3. Initial and Terminal Object
  • 3.1. Universal Property
  • 3.2. Duality
  • 3.3. Other interesting category
  • 3.4. Hom set and global element
  • 3.5. Solutions
• 4. Isomorphism
  • 4.1. A categorical view of bijections
  • 4.2. Monomorphism
  • 4.3. Epimorphism
  • 4.4. Isomorphism
  • 4.5. Solutions
• 5. Product, Coproduct, Exponential
  • 5.1. Product
  • 5.2. Coproduct
  • 5.3. Exponential
  • 5.4. Cartesian closed category
  • 5.5. Solutions
• 6. Functor and Natural Transformation
  • 6.1. Functor
  • 6.2. Endomorphism and Endofunctor
  • 6.3. Natural transformation
  • 6.4. Equivalent categories
  • 6.5. Solutions
• 7. Constructions
  • 7.1. Set and class
  • 7.2. Functor category
  • 7.3. Morphism category
  • 7.4. Presheaf
  • 7.5. Solutions
• 8. Yoneda’s Lemma
  • 8.1. Presheaves
  • 8.2. Representable functors
  • 8.3. Yoneda embedding
  • 8.4. Yoneda’s Lemma
  • 8.5. Solutions
• 9. Limit
  • 9.1. Diagram
  • 9.2. Cone
  • 9.3. Limit
  • 9.4. Diagram as functor
  • 9.5. Cone as natural transformation
  • 9.6. Solutions
• 10. References
• 11. Glossary
  • 11.1. Acronyms
  • 11.2. Nomenclature
  • 11.3. Categories
• 12. Index