The Stacks project

Lemma 37.63.4. Any quasi-affine morphism is ind-quasi-affine. Any immersion is ind-quasi-affine.

Proof. The first assertion is immediate from the definitions. In particular, affine morphisms, such as closed immersions, are ind-quasi-affine. Thus, by Lemma 37.63.3, it remains to show that an open immersion is ind-quasi-affine. This, however, is immediate from the definitions. $\square$

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