Item 2 (00DL) — 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`

Adjointness I. We have an adjunction
witnessed by a bijection of sets
\[ \textup{Hom}_{\mathsf{Sets}_{*}}\webleft (X\lhd Y,Z\webright )\cong \textup{Hom}_{\mathsf{Sets}_{*}}\webleft (X,\webleft [Y,Z\webright ]^{\lhd }_{\mathsf{Sets}_{*}}\webright ) \]

natural in $\webleft (X,x_{0}\webright ),\webleft (Y,y_{0}\webright ),\webleft (Z,z_{0}\webright )\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$, where $\webleft [X,Y\webright ]^{\lhd }_{\mathsf{Sets}_{*}}$ is the pointed set of Definition 4.3.2.1.1.

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