TITLE: Does there exist a full and faithful embedding of $\mathsf{Poset}$ in $\mathsf{Set}$?
QUESTION [6 upvotes]: Does there exist a full and faithful embedding of the category of posets into the category of sets?  I suspect no, but I don't know how to prove or disprove this.

REPLY [27 votes]: The poset $\{0,1\}$ with $0<1$ has three endomorphisms. Since there is no set with exactly three endomorphisms, there cannot be a fully faithful embedding of posets into sets.