CatDat

• notation: $\Hom(-,2)$ : $\Set^{\op}$ → $\Set$
• Source: dual of the category of sets
• Target: category of sets
• Related functors: $P$
• nLab Link

This functor maps a set $X$ to its power set $P(X)$ and a map of sets $f : X \to Y$ to the induced preimage operator $f^* : P(Y) \to P(X)$. It is isomorphic to the representable functor $\Hom(-,2) : \Set^{\op} \to \Set$.