Item 1 (00AC) — The Clowder Project

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Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
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*To be replaced with Linus Romer's Elemaints when it is released.

Functoriality. The assignments
\[ \webleft (X,x_{0}\webright ),\webleft (Y,y_{0}\webright ),\webleft (\webleft (X,x_{0}\webright ),\webleft (Y,y_{0}\webright )\webright )\mapsto \webleft (X\times Y,\webleft (x_{0},y_{0}\webright )\webright ) \]

define functors

\[ \begin{array}{ccc} A\times -\colon \mkern -15mu & \mathsf{Sets}_{*} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Sets}_{*},\\ -\times B\colon \mkern -15mu & \mathsf{Sets}_{*} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Sets}_{*},\\ -_{1}\times -_{2}\colon \mkern -15mu & \mathsf{Sets}_{*}\times \mathsf{Sets}_{*} \mkern -17.5mu& {}\mathbin {\to }\mathsf{Sets}_{*}, \end{array} \]

defined in the same way as the functors of Chapter 2: Constructions With Sets, Item 1 of Proposition 2.1.3.1.3.

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