The Clowder Project

4.1 Limits of Sets

• Subsection 4.1.1: The Terminal Set
  • Definition 4.1.1.1.1: The Terminal Set
  • Construction 4.1.1.1.2: Construction of the Terminal Set
• Subsection 4.1.2: Products of Families of Sets
  • Definition 4.1.2.1.1: The Product of a Family of Sets
  • Construction 4.1.2.1.2: Construction of the Product of a Family of Sets
  • Remark 4.1.2.1.3: Unwinding Construction 4.1.2.1.2
  • Proposition 4.1.2.1.4: Properties of Products of Families of Sets
• Subsection 4.1.3: Binary Products of Sets
  • Definition 4.1.3.1.1: Binary Products of Sets
  • Construction 4.1.3.1.2: Construction of Binary Products of Sets
  • Proposition 4.1.3.1.3: Properties of Products of Sets
  • Remark 4.1.3.1.4: The Cartesian Product of Sets as an $\webleft (\mathbb {E}_{k},\mathbb {E}_{\ell }\webright )$-Tensor Product
  • Remark 4.1.3.1.5: Diagrams for Item 9, Item 10, Item 11, and Item 12 of Proposition 4.1.3.1.3
• Subsection 4.1.4: Pullbacks
  • Definition 4.1.4.1.1: Pullbacks of Sets
  • Construction 4.1.4.1.2: Construction of Pullbacks of Sets
  • Remark 4.1.4.1.3: Pullbacks of Sets Depend on the Maps
  • Example 4.1.4.1.4: Examples of Pullbacks of Sets
  • Proposition 4.1.4.1.5: Properties of Pullbacks of Sets
• Subsection 4.1.5: Equalisers
  • Definition 4.1.5.1.1: Equalisers of Sets
  • Construction 4.1.5.1.2: Construction of Equalisers of Sets
  • Proposition 4.1.5.1.3: Properties of Equalisers of Sets
• Subsection 4.1.6: Inverse Limits
  • Definition 4.1.6.1.1: Inverse Limits of Sets
  • Construction 4.1.6.1.2: Construction of Inverse Limits of Sets
  • Example 4.1.6.1.3: Examples of Inverse Limits of Sets