Remark 98.25.1 (0GE2): Warning—The Stacks project

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Part 7: Algebraic Stacks
Chapter 98: Artin's Axioms
Section 98.25: Limit preserving functors on Noetherian schemes
Remark 98.25.1: Warning (cite)

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Remark 98.25.1 (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 110.60 for an example in case $\tau = fppf$.

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