The Stacks project

More examples of pure modules

	In particular it turns out that if we have R ---> S and N an
	S-module which is countably generated and Mittag-Leffler as an
	R-module, then it is pure relative to S/R. This finally puts a
	direct link between purity and the Mittag-Leffler condition
	which I was looking for.

	Note that there is an example that shows that one cannot go the
	other way. Namely, there exist pure modules over S/R (even when
	everything of finite type and Noetherian) which are not
	Mittag-Leffler.

Fix an example

	Actually the example was correct but the thing it was a counter
	example against was formulated incorrectly. Now we added it as
	an actual lemma in more-morphisms.tex

Tags: Added new tags

First projectivity result

	as stated this lemma can be used to proceed by Noetherian
	induction on the base in certain situations.