Power set functor

A functor 𝒫:Set→Set is a covariant functor when it takes image, and a contravariant functor when it takes preimage.

pf.

Let's say it takes image.

For sets A, B, C and functions f:A→B, g:B→C and F(f):𝒫*(A)→𝒫*(B), F(g):𝒫*(B)→𝒫*(C) and a subset α⊂A

a=b

=c