Item 2 (00D3) — The Clowder Project

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*To be replaced with Linus Romer's Elemaints when it is released.

Adjointness I. We have an adjunction
witnessed by a bijection
\[ \mathsf{Sets}^{\mathsf{op}}_{*}\webleft (A\pitchfork X,K\webright )\cong \mathsf{Sets}\webleft (A,\mathsf{Sets}_{*}\webleft (K,X\webright )\webright ), \]

i.e. by a bijection

\[ \mathsf{Sets}_{*}\webleft (K,A\pitchfork X\webright )\cong \mathsf{Sets}\webleft (A,\mathsf{Sets}_{*}\webleft (K,X\webright )\webright ), \]

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

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