The Clowder Project

9.6 Conditions on Functors

• Subsection 9.6.1: Faithful Functors
  • Definition 9.6.1.1.1: Faithful Functors
  • Proposition 9.6.1.1.2: Properties of Faithful Functors
• Subsection 9.6.2: Full Functors
  • Definition 9.6.2.1.1: Full Functors
  • Proposition 9.6.2.1.2: Properties of Full Functors
  • Question 9.6.2.1.3: Better Characterisations of Functors With Full Precomposition
• Subsection 9.6.3: Fully Faithful Functors
  • Definition 9.6.3.1.1: Fully Faithful Functors
  • Proposition 9.6.3.1.2: Properties of Fully Faithful Functors
• Subsection 9.6.4: Conservative Functors
  • Definition 9.6.4.1.1: Conservative Functors
  • Proposition 9.6.4.1.2: Properties of Conservative Functors
  • Question 9.6.4.1.3: Characterisations of Functors With Conservative Pre/Postcomposition
• Subsection 9.6.5: Essentially Injective Functors
  • Definition 9.6.5.1.1: Essentially Injective Functors
  • Question 9.6.5.1.2: Characterisations of Functors With Essentially Injective Pre/Postcomposition
• Subsection 9.6.6: Essentially Surjective Functors
  • Definition 9.6.6.1.1: Essentially Surjective Functors
  • Question 9.6.6.1.2: Characterisations of Functors With Essentially Surjective Pre/Postcomposition
• Subsection 9.6.7: Equivalences of Categories
  • Definition 9.6.7.1.1: Equivalences of Categories
  • Proposition 9.6.7.1.2: Properties of Equivalences of Categories
• Subsection 9.6.8: Isomorphisms of Categories
  • Definition 9.6.8.1.1: Isomorphisms of Categories
  • Example 9.6.8.1.2: Equivalent But Non-Isomorphic Categories
  • Proposition 9.6.8.1.3: Properties of Isomorphisms of Categories