Item 6 (00T5) — The Clowder Project

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Style 1	`book`	Alegreya Sans	`tcbthm`
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*To be replaced with Linus Romer's Elemaints when it is released.

1. Symmetric Strict Monoidality With Respect to Intersections. The direct image function of Item 1 has a symmetric strict monoidal structure
$(R_{!}, R_{!}^{\otimes}, R_{! | 1}^{\otimes}) : (P (A), \cap, A) \to (P (B), \cap, B),$

being equipped with equalities

$\begin{matrix} R_{! | U, V}^{\otimes} : R_{!} (U \cap V) \overset{=}{\to} R_{!} (U) \cap R_{!} (V), \\ R_{! | 1}^{\otimes} : R_{!} (A) \overset{=}{\to} B, \end{matrix}$

natural in $U, V \in P (A)$ .

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