The Clowder Project

2.2 Colimits of Sets

• Subsection 2.2.1: The Initial Set
  • Definition 2.2.1.1.1: The Initial Set
  • Construction 2.2.1.1.2: Construction of the Initial Set
• Subsection 2.2.2: Coproducts of Families of Sets
  • Definition 2.2.2.1.1: The Coproduct of a Family of Sets
  • Construction 2.2.2.1.2: Construction of the Coproduct of a Family of Sets
  • Proposition 2.2.2.1.3: Properties of Coproducts of Families of Sets
• Subsection 2.2.3: Binary Coproducts
  • Definition 2.2.3.1.1: Coproducts of Sets
  • Construction 2.2.3.1.2: Construction of Coproducts of Sets
  • Proposition 2.2.3.1.3: Properties of Coproducts of Sets
• Subsection 2.2.4: Pushouts
  • Definition 2.2.4.1.1: Pushouts of Sets
  • Construction 2.2.4.1.2: Construction of Pushouts of Sets
  • Remark 2.2.4.1.3: Unwinding Definition 2.2.4.1.1
  • Remark 2.2.4.1.4: Pushouts of Sets Depend on the Maps
  • Example 2.2.4.1.5: Examples of Pushouts of Sets
  • Proposition 2.2.4.1.6: Properties of Pushouts of Sets
• Subsection 2.2.5: Coequalisers
  • Definition 2.2.5.1.1: Coequalisers of Sets
  • Construction 2.2.5.1.2: Construction of Coequalisers of Sets
  • Remark 2.2.5.1.3: Unwinding Definition 2.2.5.1.1
  • Example 2.2.5.1.4: Examples of Coequalisers of Sets
  • Proposition 2.2.5.1.5: Properties of Coequalisers of Sets
• Subsection 2.2.6: Direct Colimits
  • Definition 2.2.6.1.1: Direct Colimits of Sets
  • Construction 2.2.6.1.2: Construction of Direct Colimits of Sets
  • Lemma 2.2.6.1.3: Identification of $x$ with $f_{\alpha \beta }\webleft (x\webright )$ in Direct Colimits
  • Example 2.2.6.1.4: Examples of Direct Colimits of Sets