3.2.2 The Monoidal Unit

Definition 3.2.2.1.1 ▶ The Monoidal Unit of $\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}$

The monoidal unit of the coproduct of sets is the functor

\[ \mathbb {0}^{\mathsf{Sets}} \colon \mathsf{pt}\to \mathsf{Sets} \]

defined by

\[ \mathbb {0}_{\mathsf{Sets}}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\text{Ø}, \]

where $\text{Ø}$ is the empty set of Chapter 2: Constructions With Sets, Definition 2.3.1.1.1.

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