Does an Equivalence Between Categories C and D imply an Equivalence Between D and C?

Question

According to Wikipedia:

Formally, given two categories C and D, an equivalence of categories consists of a functor F : C → D, a functor G : D → C, and two natural isomorphisms ε: FG→ID and η : IC→GF. Here FG: D→D and GF: C→C, denote the respective compositions of F and G, and IC: C→C and ID: D→D denote the identity functors on C and D, assigning each object and morphism to itself.

Let the notation $C \sim D$ imply that functors $F$ and $G$ exist as above (with natural isomorphisms $\varepsilon$ and $\eta$).

Question: Does $C \sim D$ imply that $D \sim C$?

Answer 1

Yes, just switch the roles of $F$ and $G$ and invert the natural isomorphisms.