I have a very quick question. Is there an easy example of a representable presheaf on a site that is not a sheaf? This certainly can't happen on a small FPPF site so I would expect a counterexample to arise on the big Zariski site. 


Thanks!



Representable Presheaf
Since you ask specifically for an *easy* example (not a natural, useful, etc., one), I suggest taking any category in which there are two objects $A$ and $B$ for which Hom$(A,B)$ is not a one-element set (i.e., the category is equivalent to neither the initial nor the terminal category) and giving it the topology in which every sieve (even the empty sieve) is covering. Then the only sheaf is the functor assigning, to each object, a singleton set, and my assumption about $A$ and $B$ ensures that the presheaf represented by $A$ is not a sheaf.


