Remark 85.4.1. In Situation 85.3.3 an augmentation a_0 towards a site \mathcal{D} will mean
a_0 : \mathcal{C}_0 \to \mathcal{D} is a morphism of sites given by a continuous functor u_0 : \mathcal{D} \to \mathcal{C}_0 such that for all \varphi , \psi : [0] \to [n] we have u_\varphi \circ u_0 = u_\psi \circ u_0.
a_0 : \mathop{\mathit{Sh}}\nolimits (\mathcal{C}_0) \to \mathop{\mathit{Sh}}\nolimits (\mathcal{D}) is a morphism of topoi given by a cocontinuous functor u_0 : \mathcal{C}_0 \to \mathcal{D} such that for all \varphi , \psi : [0] \to [n] we have u_0 \circ u_\varphi = u_0 \circ u_\psi .
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