Item 2 (00GF) — 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. We have adjunctions
witnessed by bijections
\begin{align*} \textup{Hom}_{\mathsf{Sets}_{*}}\webleft (X\wedge Y,Z\webright ) & \cong \textup{Hom}_{\mathsf{Sets}_{*}}\webleft (X,\textbf{Sets}_{*}\webleft (Y,Z\webright )\webright ),\\ \textup{Hom}_{\mathsf{Sets}_{*}}\webleft (X\wedge Y,Z\webright ) & \cong \textup{Hom}_{\mathsf{Sets}_{*}}\webleft (X,\textbf{Sets}_{*}\webleft (A,Z\webright )\webright ), \end{align*}

natural in $\webleft (X,x_{0}\webright ),\webleft (Y,y_{0}\webright ),\webleft (Z,z_{0}\webright )\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$.

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