The Stacks project

Remove sentence

Thanks to KDD
https://stacks.math.columbia.edu/tag/03I2#comment-10025

Whitespace changes

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.

LaTeX: \Sch

	Introduced a new macro

	\def\Sch{\textit{Sch}}

	and replaced all the occurences of \textit{Sch} with \Sch.

End conversion of etale to \'etale.

Algebraic Stacks: Making the definition work.

	This is a rather large set of changes. It turns out that we need
	to repeat some of the work done in the setting of schemes in the
	setting of algebraic spaces. We can do this as we go along, but
	we need to have the framework in place with some example
	sections. Hence added to the project are a chapter on topologies
	on algebraic spaces and a chapter on descent and algebraic
	spaces. We further need to add much more material to the section
	on morphisms of algebraic spaces, since right now we do not even
	cover the notion of a smooth morphism of algebraic spaces.

	Of course most of this is a simple matter of pointing out the
	relevant results on schemes. Still...

Tags: New tags added and two fixed

Spaces: Etale locally representable map sometimes representable

	Given an algebraic space X and a sheaf F and a tranformation
	F --> X which after an etale covering becomes representable and
	lies in a class of morphisms P which satisfy effective descent
	for etale coverings, then F is an algebraic space, F --> X is
	representable and has P.