Lemma 60.8.2. In Situation 60.7.5. The category $\text{CRIS}(X/S)$ has all finite nonempty limits, in particular products of pairs and fibre products. The functor (60.8.1.1) commutes with limits.

**Proof.**
Omitted. Hint: See Lemma 60.5.3 for the affine case. See also Divided Power Algebra, Remark 23.3.5.
$\square$

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