Item 1 (018U) — 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 $\mathcal{C},\mathcal{D},\webleft (\mathcal{C},\mathcal{D}\webright )\mapsto \mathsf{Fun}\webleft (\mathcal{C},\mathcal{D}\webright )$ define functors
\[ \begin{array}{ccc} \mathsf{Fun}\webleft (\mathcal{C},-\webright )\colon \mkern -15mu & \mathsf{Cats} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Cats},\\ \mathsf{Fun}\webleft (-,\mathcal{D}\webright )\colon \mkern -15mu & \mathsf{Cats}\mathrlap {{}^{\mathsf{op}}} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Cats},\\ \mathsf{Fun}\webleft (-_{1},-_{2}\webright )\colon \mkern -15mu & \mathsf{Cats}^{\mathsf{op}}\times \mathsf{Cats} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Cats}. \end{array} \]

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