Remark 60.8.6 (Comparison with Zariski site). In Situation 60.7.5. The functor (220.127.116.11) is cocontinuous (details omitted) and commutes with products and fibred products (Lemma 60.8.2). Hence we obtain a morphism of topoi
from the big crystalline topos of $X/S$ to the big Zariski topos of $X$. See Sites, Section 7.21.