  We show that Weak Vop\v{e}nka's Principle, which is the statement that the
opposite category of ordinals cannot be fully embedded into the category of
graphs, is equivalent to the large cardinal principle Ord is Woodin, which says
that for every class C there is a C-strong cardinal. Weak Vop\v{e}nka's
Principle was already known to imply the existence of a proper class of
measurable cardinals. We improve this lower bound to the optimal one by
defining structures whose nontrivial homomorphisms can be used as extenders,
thereby producing elementary embeddings witnessing C-strongness of some
cardinal.
