A Grothendieck topology on $\Delta$

Question

Is there a choice for a Grothendieck topology on $\Delta$ for which most interesting simplicial sets are sheaves (like representables, horns and boundaries, and more generally all categories)? I suspect I can look at the Segal condition as a sheaf condition, but I'm not able to go further, nor I find information googling something similar to my question (which is, I admit it, somewhat vague).