The Clowder Project

8.1 Relations

• Subsection 8.1.1: Foundations
  • Definition 8.1.1.1.1: Relations
  • Remark 8.1.1.1.2: Unwinding Item 1, I
  • Remark 8.1.1.1.3: Unwinding Item 2, II
  • Notation 8.1.1.1.4: Further Notation for Relations
  • Example 8.1.1.1.5: The Trivial Relation
  • Example 8.1.1.1.6: The Cotrivial Relation
  • Example 8.1.1.1.7: The Characteristic Relation of a Set
  • Proposition 8.1.1.1.8: Properties of Relations
• Subsection 8.1.2: Relations as Decategorifications of Profunctors
  • Remark 8.1.2.1.1: Relations as Decategorifications of Profunctors I
  • Remark 8.1.2.1.2: Relations as Decategorifications of Profunctors II
• Subsection 8.1.3: Composition of Relations
  • Definition 8.1.3.1.1: Composition of Relations
  • Example 8.1.3.1.2: Examples of Composition of Relations
  • Proposition 8.1.3.1.3: Properties of Composition of Relations
• Subsection 8.1.4: Apartness Composition of Relations
  • Definition 8.1.4.1.1: Apartness Composition of Relations
• Subsection 8.1.5: The Converse of a Relation
  • Definition 8.1.5.1.1: The Converse of a Relation
  • Example 8.1.5.1.2: Examples of Converses of Relations
  • Proposition 8.1.5.1.3: Properties of Converses of Relations