Remark 72.19.5. Using Lemma 72.19.4 and the work done in the earlier sections of this chapter it is easy to make a list of types of morphisms which are smooth local on the source-and-target. In each case we list the lemma which implies the property is smooth local on the source and the lemma which implies the property is smooth local on the target. In each case the third assumption of Lemma 72.19.4 is trivial to check, and we omit it. Here is the list:

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