The Clowder Project

5.1 Relations

• Subsection 5.1.1: Foundations
  • Definition 5.1.1.1.1: Relations
  • Notation 5.1.1.1.2: Further Notation for Relations
  • Definition 5.1.1.1.3: The Po/Set of Relations Over Two Sets
  • Remark 5.1.1.1.4: Equivalent Definitions of Relations
  • Proposition 5.1.1.1.5: Properties of Relations
• Subsection 5.1.2: Relations as Decategorifications of Profunctors
  • Remark 5.1.2.1.1: Relations as Decategorifications of Profunctors I
  • Remark 5.1.2.1.2: Relations as Decategorifications of Profunctors II
• Subsection 5.1.3: Examples of Relations
  • Example 5.1.3.1.1: The Trivial Relation
  • Example 5.1.3.1.2: The Cotrivial Relation
  • Example 5.1.3.1.3: The Characteristic Relation of a Set
  • Example 5.1.3.1.4: Square Roots
  • Example 5.1.3.1.5: Complex Logarithms
  • Example 5.1.3.1.6: More Examples of Relations
• Subsection 5.1.4: Functional Relations
  • Definition 5.1.4.1.1: Functional Relations
  • Proposition 5.1.4.1.2: Properties of Functional Relations
• Subsection 5.1.5: Total Relations
  • Definition 5.1.5.1.1: Total Relations
  • Proposition 5.1.5.1.2: Properties of Total Relations