Item 1 (003D) — 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 assignments $X,Y,\webleft (X,Y\webright )\mapsto \textup{Hom}_{\mathsf{Sets}}\webleft (X,Y\webright )$ define functors
\[ \begin{array}{ccc} \mathsf{Sets}\webleft (X,-\webright )\colon \mkern -15mu & \mathsf{Sets} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Sets},\\ \mathsf{Sets}\webleft (-,Y\webright )\colon \mkern -15mu & \mathsf{Sets}^{\mathrlap {\mathsf{op}}} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Sets},\\ \mathsf{Sets}\webleft (-_{1},-_{2}\webright )\colon \mkern -15mu & \mathsf{Sets}^{\mathsf{op}}\times \mathsf{Sets} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Sets}. \end{array} \]

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