Item 1 (0052) — 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 $U\mapsto U^{\textsf{c}}$ defines a functor
\[ \webleft (-\webright )^{\textsf{c}}\colon \mathcal{P}\webleft (X\webright )^{\mathsf{op}}\to \mathcal{P}\webleft (X\webright ). \]

In particular, the following statements hold for each $U,V\in \mathcal{P}\webleft (X\webright )$:
- If $U\subset V$, then $V^{\textsf{c}}\subset U^{\textsf{c}}$.

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