The Clowder Project

7.2 Kan Extensions and Kan Lifts in the $2$-Category of Relations

• Subsection 7.2.1: Left Kan Extensions in $\textbf{Rel}$
  • Proposition 7.2.1.1.1: Left Kan Extensions in $\textbf{Rel}$
  • Question 7.2.1.1.2: Existence of Specific Left Kan Extensions of Relations
  • Question 7.2.1.1.3: Explicit Description of Left Kan Extensions Along Functions
• Subsection 7.2.2: Left Kan Lifts in $\textbf{Rel}$
  • Proposition 7.2.2.1.1: Left Kan Lifts in $\textbf{Rel}$
  • Question 7.2.2.1.2: Existence of Specific Left Kan Lifts of Relations
  • Question 7.2.2.1.3: Explicit Description of Left Kan Lifts Along Functions
• Subsection 7.2.3: Right Kan Extensions in $\textbf{Rel}$
  • Proposition 7.2.3.1.1: Existence of Right Kan Extensions in $\textbf{Rel}$
• Subsection 7.2.4: Right Kan Lifts in $\textbf{Rel}$
  • Proposition 7.2.4.1.1: Existence of Right Kan Lifts in $\textbf{Rel}$