= Exponential in a presheaf category
{title2=$(Q^P)(c)=\operatorname{Nat}(H_c\times P,Q)$}
For <categorical presheaves> $P,Q$ on a <small category>, restrictions in the displayed <exponential object> act by precomposition with $H_u\times1_P$. Evaluation sends $(\alpha,x)$ at $c$ to $\alpha_c(1_c,x)$. The <currying> of $t:R\times P\to Q$ sends $z\in R(c)$ to the natural transformation whose value on $(v:a\to c,x\in P(a))$ is $t_a(R(v)z,x)$. Evaluation and currying are inverse and natural, proving the <Cartesian closed category> structure.
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