Item 1 (008S) — 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`

Functoriality. The assignment $U\mapsto f_{!}\webleft (U\webright )$ defines a functor
\[ f_{!}\colon \webleft (\mathcal{P}\webleft (X\webright ),\subset \webright )\to \webleft (\mathcal{P}\webleft (Y\webright ),\subset \webright ). \]

In particular, for each $U,V\in \mathcal{P}\webleft (X\webright )$, the following condition is satisfied:
- If $U\subset V$, then $f_{!}\webleft (U\webright )\subset f_{!}\webleft (V\webright )$.

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