Item 4 (01J7) — 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 I. The map
is an isomorphism 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.

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