Item 1 (00QM) — 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 $R\mapsto R^{\dagger }$ defines a functor (i.e. morphism of posets)
\[ \webleft (-\webright )^{\dagger }\colon \mathbf{Rel}\webleft (A,B\webright )\to \mathbf{Rel}\webleft (B,A\webright ). \]

In particular, given relations $R,S\colon A\mathrel {\rightrightarrows \kern -9.5pt\mathrlap {|}\kern 6pt}B$, we have:
- If $R\subset S$, then $R^{\dagger }\subset S^{\dagger }$.

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