Proposition 4.3.2.1.2 (00B3): Properties of Coproducts of Families of Pointed Sets

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Table of Contents
Part 1: Sets
Chapter 4: Pointed Sets
Section 4.3: Colimits of Pointed Sets
Subsection 4.3.2: Coproducts of Families of Pointed Sets
Proposition 4.3.2.1.2: Properties of Coproducts of Families of Pointed Sets (cite)

Let $\webleft\{ \webleft (X_{i},x^{i}_{0}\webright )\webright\} _{i\in I}$ be a family of pointed sets.

Functoriality. The assignment $\webleft\{ \webleft (X_{i},x^{i}_{0}\webright )\webright\} _{i\in I}\mapsto \webleft (\bigvee _{i\in I}X_{i},p_{0}\webright )$ defines a functor
\[ \bigvee _{i\in I}\colon \mathsf{Fun}\webleft (I_{\mathsf{disc}},\mathsf{Sets}_{*}\webright )\to \mathsf{Sets}_{*}. \]

Proof of Proposition 4.3.2.1.2.

Item 1: Functoriality

This follows from

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