# Powerset functor

A powerset functor, `𝒫 : 𝗦𝗲𝘁 → 𝗦𝗲𝘁`, sends subsets to their image under maps.

∀A,B ∈ Obj(𝗦𝗲𝘁), f : A → B and S ⊂ A:\
𝒫 A = 𝒫(A),\
𝒫 f : 𝒫(A) → 𝒫(B), S ⟼ f(S)

𝗦𝗲𝘁 is a category of sets. The objects are all small sets, and the arrows are functions between sets.


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