The Clowder Project

5.3 Properties of the $2$-Category of Relations

• Subsection 5.3.1: Self-Duality
  • Proposition 5.3.1.1.1: Self-Duality for the (2-)Category of Relations
• Subsection 5.3.2: Isomorphisms and Equivalences in $\textbf{Rel}$
  • Proposition 5.3.2.1.1: Isomorphisms and Equivalences in $\textbf{Rel}$
• Subsection 5.3.3: Adjunctions in $\textbf{Rel}$
  • Proposition 5.3.3.1.1: Adjunctions in $\textbf{Rel}$
• Subsection 5.3.4: Monads in $\textbf{Rel}$
  • Proposition 5.3.4.1.1: Monads in $\textbf{Rel}$
• Subsection 5.3.5: Comonads in $\textbf{Rel}$
  • Proposition 5.3.5.1.1: Comonads in $\textbf{Rel}$
• Subsection 5.3.6: Co/Monoids in $\textbf{Rel}$
  • Remark 5.3.6.1.1: Co/Monoids in $\textbf{Rel}$
• Subsection 5.3.7: Monomorphisms in $\mathsf{Rel}$
  • Proposition 5.3.7.1.1: Characterisations of Monomorphisms in $\mathsf{Rel}$
• Subsection 5.3.8: 2-Categorical Monomorphisms in $\textbf{Rel}$
  • Proposition 5.3.8.1.1: 2-Categorical Monomorphisms in $\textbf{Rel}$
  • Question 5.3.8.1.2: Better Characterisations of Representably Full Morphisms in $\textbf{Rel}$
• Subsection 5.3.9: Epimorphisms in $\mathsf{Rel}$
  • Proposition 5.3.9.1.1: Characterisations of Epimorphisms in $\mathsf{Rel}$
• Subsection 5.3.10: 2-Categorical Epimorphisms in $\textbf{Rel}$
  • Proposition 5.3.10.1.1: 2-Categorical Epimorphisms in $\textbf{Rel}$
  • Question 5.3.10.1.2: Better Characterisations of Corepresentably Full Morphisms in $\textbf{Rel}$
• Subsection 5.3.11: Co/Limits in $\mathsf{Rel}$
  • Proposition 5.3.11.1.1: Co/Limits in $\mathsf{Rel}$
• Subsection 5.3.12: Kan Extensions and Kan Lifts in $\textbf{Rel}$
  • Remark 5.3.12.1.1: Kan Extensions and Kan Lifts in $\textbf{Rel}$
• Subsection 5.3.13: Closedness of $\textbf{Rel}$
  • Proposition 5.3.13.1.1: Closedness of $\textbf{Rel}$
• Subsection 5.3.14: $\textbf{Rel}$ as a Category of Free Algebras
  • Proposition 5.3.14.1.1: $\textbf{Rel}$ as a Category of Free Algebras