The Stacks project

LaTeX: \Ob

	Introduced a macro

	\def\Ob{\mathop{\rm Ob}\nolimits}

	and replaced any occurence of \text{Ob}( with \Ob(. There are
	still some occurences of \text{Ob} but these are sets, not the
	operator that takes the set of objects of a category.

Fixed references to short titles

	using the script we will add in the next commit

Criteria for quotient stacks to be algebraic

	The most interesting result is that [S/G] is an algebraic stack
	if and only if G ---> S is flat and locally of finite
	presentation. The proof uses a fun lemma on the descent of
	flatness (see the change in descent.tex).

Terminology:
	"group space" ---> "group algebraic space"
	"groupoid space" ---> "groupoid in algebraic spaces"

	It seems more natural this way to at least three people, and in
	any case it prevents the possible confusion that may arise from
	the fact that in some places in the literature the word "space"
	sometimes refers to any sheaf on schemes in the fppf topology.

Tags: added new tags

Restriction and equivalences

	We inserted a couple of lemmas describing when the restriction
	of a groupoid scheme gives rise to an isomorphic quotient sheaf
	or when it gives rise to an equivalent quotient stack.