The Stacks project

Remark 7.14.8. The conditions of Proposition 7.14.7 above are equivalent to saying that $u$ is left exact, i.e., commutes with finite limits. See Categories, Lemmas 4.18.4 and 4.23.2. It seems more natural to phrase it in terms of final objects and fibre products since this seems to have more geometric meaning in the examples.

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