Item 3 (00SG) — The Clowder Project

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Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
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*To be replaced with Linus Romer's Elemaints when it is released.

1. Preservation of Colimits. We have an equality of sets
$R^{- 1} (⋃_{i \in I} U_{i}) = ⋃_{i \in I} R^{- 1} (U_{i}),$

natural in ${U_{i}}_{i \in I} \in P (B)^{\times I}$ . In particular, we have equalities

$\begin{matrix} R^{- 1} (U) \cup R^{- 1} (V) = R^{- 1} (U \cup V), \\ R^{- 1} (Ø) = Ø, \end{matrix}$

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

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