3 Pointed Sets
This chapter contains some foundational material on pointed sets.

Section 3.1: Pointed Sets

Subsection 3.1.1: Foundations

Subsection 3.1.2: Morphisms of Pointed Sets

Subsection 3.1.3: The Category of Pointed Sets

Subsection 3.1.4: Elementary Properties of Pointed Sets

Proposition 3.1.4.1.1: Elementary Properties of Pointed Sets

Section 3.2: Limits of Pointed Sets

Subsection 3.2.1: The Terminal Pointed Set

Definition 3.2.1.1.1: The Terminal Pointed Set

Subsection 3.2.2: Products of Families of Pointed Sets

Definition 3.2.2.1.1: The Product of a Family of Pointed Sets

Proposition 3.2.2.1.2: Properties of Products of Families of Pointed Sets

Subsection 3.2.3: Products

Definition 3.2.3.1.1: Products of Pointed Sets

Proposition 3.2.3.1.2: Properties of Products of Pointed Sets

Subsection 3.2.4: Pullbacks

Definition 3.2.4.1.1: Pullbacks of Pointed Sets

Proposition 3.2.4.1.2: Properties of Pullbacks of Pointed Sets

Subsection 3.2.5: Equalisers

Definition 3.2.5.1.1: Equalisers of Pointed Sets

Proposition 3.2.5.1.2: Properties of Equalisers of Pointed Sets

Section 3.3: Colimits of Pointed Sets

Subsection 3.3.1: The Initial Pointed Set

Definition 3.3.1.1.1: The Initial Pointed Set

Subsection 3.3.2: Coproducts of Families of Pointed Sets

Definition 3.3.2.1.1: Coproducts of Families of Pointed Sets

Proposition 3.3.2.1.2: Properties of Coproducts of Families of Pointed Sets

Subsection 3.3.3: Coproducts

Definition 3.3.3.1.1: Coproducts of Pointed Sets

Proposition 3.3.3.1.2: Properties of Wedge Sums of Pointed Sets

Subsection 3.3.4: Pushouts

Definition 3.3.4.1.1: Pushouts of Pointed Sets

Proposition 3.3.4.1.2: Properties of Pushouts of Pointed Sets

Subsection 3.3.5: Coequalisers

Definition 3.3.5.1.1: Coequalisers of Pointed Sets

Proposition 3.3.5.1.2: Properties of Coequalisers of Pointed Sets

Section 3.4: Constructions With Pointed Sets

Subsection 3.4.1: Free Pointed Sets

Definition 3.4.1.1.1: Free Pointed Sets

Proposition 3.4.1.1.2: Properties of Free Pointed Sets