The Clowder Project

9.4 Groupoids

• Subsection 9.4.1: Isomorphisms
  • Definition 9.4.1.1.1: Isomorphisms
  • Notation 9.4.1.1.2: The Set of Isomorphisms Between Two Objects in a Category
• Subsection 9.4.2: Groupoids
  • Definition 9.4.2.1.1: Groupoids
  • Example 9.4.2.1.2: Groups as One-Object Groupoids
• Subsection 9.4.3: The Groupoid Completion of a Category
  • Definition 9.4.3.1.1: The Groupoid Completion of a Category
  • Construction 9.4.3.1.2: Construction of the Groupoid Completion of a Category
  • Proposition 9.4.3.1.3: Properties of Groupoid Completion
• Subsection 9.4.4: The Core of a Category
  • Definition 9.4.4.1.1: The Core of a Category
  • Notation 9.4.4.1.2: Alternative Notation for the Core of a Category
  • Construction 9.4.4.1.3: Construction of the Core of a Category
  • Proposition 9.4.4.1.4: Properties of the Core of a Category