The Clowder Project

8.4 Properties of the $2$-Category of Relations

• Subsection 8.4.1: Self-Duality
  • Proposition 8.4.1.1.1: Self-Duality for the (2-)Category of Relations
• Subsection 8.4.2: Isomorphisms and Equivalences
  • Proposition 8.4.2.1.1: Isomorphisms and Equivalences in $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.3: Internal Adjunctions
  • Proposition 8.4.3.1.1: Adjunctions in $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.4: Internal Monads
  • Proposition 8.4.4.1.1: Monads in $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.5: Internal Comonads
  • Proposition 8.4.5.1.1: Comonads in $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.6: Co/Monoids
  • Remark 8.4.6.1.1: Co/Monoids in $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.7: Monomorphisms
  • Proposition 8.4.7.1.1: Characterisations of Monomorphisms in $\mathsf{Rel}$
• Subsection 8.4.8: 2-Categorical Monomorphisms
  • Proposition 8.4.8.1.1: 2-Categorical Monomorphisms in $\boldsymbol {\mathsf{Rel}}$
  • Question 8.4.8.1.2: Better Characterisations of Representably Full Morphisms in $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.9: Epimorphisms
  • Proposition 8.4.9.1.1: Characterisations of Epimorphisms in $\mathsf{Rel}$
• Subsection 8.4.10: 2-Categorical Epimorphisms
  • Proposition 8.4.10.1.1: 2-Categorical Epimorphisms in $\boldsymbol {\mathsf{Rel}}$
  • Question 8.4.10.1.2: Better Characterisations of Corepresentably Full Morphisms in $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.11: Co/Limits
  • Proposition 8.4.11.1.1: Co/Limits in $\mathsf{Rel}$
• Subsection 8.4.12: Internal Kan Extensions and Lifts
  • Remark 8.4.12.1.1: Kan Extensions and Kan Lifts in $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.13: Closedness
  • Proposition 8.4.13.1.1: Closedness of $\boldsymbol {\mathsf{Rel}}$
• Subsection 8.4.14: $\mathsf{Rel}$ as a Category of Free Algebras
  • Proposition 8.4.14.1.1: $\mathsf{Rel}$ as a Category of Free Algebras