Subsection 4.5.11 (00H4): Universal Properties of the Smash Product of Pointed Sets II

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Table of Contents
Part 1: Sets
Chapter 4: Tensor Products of Pointed Sets
Section 4.5: The Smash Product of Pointed Sets
Subsection 4.5.11: Universal Properties of the Smash Product of Pointed Sets II (cite)

4.5.11 Universal Properties of the Smash Product of Pointed Sets II

Theorem 4.5.11.1.1 ▶ Universal Properties of the Smash Product of Pointed Sets II

The symmetric monoidal structure on the category $\mathsf{Sets}_{*}$ is the unique symmetric monoidal structure on $\mathsf{Sets}_{*}$ such that the free pointed set functor

\[ \webleft (-\webright )^{+} \colon \mathsf{Sets}\to \mathsf{Sets}_{*} \]

admits a symmetric monoidal structure.

Proof of Theorem 4.5.11.1.1.

See Theorem 5.1 of [Gepner–Groth–Nikolaus, Universality of Multiplicative Infinite Loop Space Machines].

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