# Bijection between hom sets of equivalent categories?

I’ve been trying to prove the following claim, but am now unsure about its truth. Is it true, and if so, where can I find a proof?

Claim: For any categories C, D, E such that C and D are equivalent,

(i) The set $$Hom($$C, E$$)$$ of functors from C to E is in bijective correspondence with the set $$Hom($$D, E$$)$$ of functors from D to E, i.e. $$Hom($$C, E$$)$$ $$simeq$$ $$Hom($$D, E$$)$$.

(ii) The set $$Hom($$E, C$$)$$ of functors from E to C is in bijective correspondence with the set $$Hom($$E, D$$)$$ of functors from E to D, i.e. $$Hom($$E, C$$)$$ $$simeq$$ $$Hom($$E, D$$)$$.