The Clowder Project

9.7 More Conditions on Functors

• Subsection 9.7.1: Dominant Functors
  • Definition 9.7.1.1.1: Dominant Functors
  • Proposition 9.7.1.1.2: Properties of Dominant Functors
  • Question 9.7.1.1.3: Characterisations of Functors With Dominant Pre/Postcomposition
• Subsection 9.7.2: Monomorphisms of Categories
  • Definition 9.7.2.1.1: Monomorphisms of Categories
  • Proposition 9.7.2.1.2: Properties of Monomorphisms of Categories
  • Question 9.7.2.1.3: Characterisations of Functors With Monic Pre/Postcomposition
• Subsection 9.7.3: Epimorphisms of Categories
  • Definition 9.7.3.1.1: Epimorphisms of Categories
  • Proposition 9.7.3.1.2: Properties of Epimorphisms of Categories
  • Question 9.7.3.1.3: Characterisations of Functors With Epic Pre/Postcomposition
• Subsection 9.7.4: Pseudomonic Functors
  • Definition 9.7.4.1.1: Pseudomonic Functors
  • Proposition 9.7.4.1.2: Properties of Pseudomonic Functors
• Subsection 9.7.5: Pseudoepic Functors
  • Definition 9.7.5.1.1: Pseudoepic Functors
  • Proposition 9.7.5.1.2: Properties of Pseudoepic Functors
  • Question 9.7.5.1.3: Characterisations of Pseudoepic Functors
  • Question 9.7.5.1.4: Must a Pseudomonic and Pseudoepic Functor Be an Equivalence of Categories
  • Question 9.7.5.1.5: Characterisations of Functors With Pseudoepic Pre/Postcomposition