Remark 97.25.1 (Warning). The site $(\textit{Noetherian}/S)_\tau$ does not have fibre products. Hence we have to be careful in working with sheaves. For example, the continuous inclusion functor $(\textit{Noetherian}/S)_\tau \to (\mathit{Sch}/S)_\tau$ does not define a morphism of sites. See Examples, Section 109.58 for an example in case $\tau = fppf$.

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