5.5.3 The Monoidal Unit

The monoidal unit of the smash product of pointed sets is the functor

\[ \mathbb {1}^{\mathsf{Sets}_{*}} \colon \mathsf{pt}\to \mathsf{Sets}_{*} \]

defined by

\[ \mathbb {1}_{\mathsf{Sets}_{*}}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}S^{0}. \]


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