The Clowder Project

8.1 Categories

• Subsection 8.1.1: Foundations
  • Definition 8.1.1.1.1: Categories
  • Notation 8.1.1.1.2: Further Notation for Morphisms in Categories
  • Definition 8.1.1.1.3: Size Conditions on Categories
• Subsection 8.1.2: Examples of Categories
  • Example 8.1.2.1.1: The Punctual Category
  • Example 8.1.2.1.2: Monoids as One-Object Categories
  • Example 8.1.2.1.3: The Empty Category
  • Example 8.1.2.1.4: Ordinal Categories
  • Example 8.1.2.1.5: More Examples of Categories
• Subsection 8.1.3: Posetal Categories
  • Definition 8.1.3.1.1: Posetal Categories
  • Proposition 8.1.3.1.2: Properties of Posetal Categories
• Subsection 8.1.4: Subcategories
  • Definition 8.1.4.1.1: Subcategories
  • Definition 8.1.4.1.2: Full Subcategories
  • Definition 8.1.4.1.3: Strictly Full Subcategories
  • Definition 8.1.4.1.4: Wide Subcategories
• Subsection 8.1.5: Skeletons of Categories
  • Definition 8.1.5.1.1: Skeletons of Categories
  • Definition 8.1.5.1.2: Skeletal Categories
  • Proposition 8.1.5.1.3: Properties of Skeletons of Categories
• Subsection 8.1.6: Precomposition and Postcomposition
  • Definition 8.1.6.1.1: Precomposition and Postcomposition Functions
  • Proposition 8.1.6.1.2: Properties of Pre/Postcomposition