Item 5 (01J8) — The Clowder Project

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

Interaction With Products II. The map
where
\[ U\boxtimes _{X\times Y}V\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ \webleft (u,v\webright )\in X\times Y\ \middle |\ \text{$u\in U$ and $v\in V$}\webright\} \]

is an inclusion of sets, natural in $X,Y\in \text{Obj}\webleft (\mathsf{Sets}\webright )$ with respect to each of the functor structures $\mathcal{P}_{*}$, $\mathcal{P}^{-1}$, and $\mathcal{P}_{!}$ on $\mathcal{P}$ of Proposition 2.4.2.1.1. Moreover, this makes $\mathcal{P}_{*}$, $\mathcal{P}^{-1}$, and $\mathcal{P}_{!}$ into symmetric monoidal functors.

Noticed something off, or have any comments? Feel free to reach out!

You can also use the contact form below: