Item 2 (01QW) — 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.

Adjoint Equivalence. We have an adjoint equivalence of categories
witnessed by a bijection of sets
\begin{align*} \mathsf{Sets}\webleft (X^{-},Y\webright )\cong \mathsf{Sets}_{*}\webleft (X,Y^{+}\webright ),\end{align*}

natural in $X\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$ and $Y\in \text{Obj}\webleft (\mathsf{Sets}\webright )$, and by isomorphisms

\begin{align*} \webleft (X^{-}\webright )^{+} & \cong X,\\ \webleft (Y^{+}\webright )^{-} & \cong Y, \end{align*}

once again natural in $X\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$ and $Y\in \text{Obj}\webleft (\mathsf{Sets}\webright )$.

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