Remark 73.21.5. Using Lemma 73.21.4 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 etale 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 73.21.4 is trivial to check, and we omit it. Here is the list:

1. étale, see Lemmas 73.19.1 and 73.11.28,

2. locally quasi-finite, see Lemmas 73.19.2 and 73.11.24,

3. unramified, see Lemmas 73.19.3 and 73.11.27, and

4. add more here as needed.

Of course any property listed in Remark 73.20.5 is a fortiori an example that could be listed here.

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