The Stacks project

Fix coding style in categories

Some grammatical errors in Categories

There are some sentences of the form, for example, “there exists a P and a Q”.
I have changed “exists” into “exist”.
There are other small changes too.

Work out Brian's suggestion properties diagonals

Thanks to Brian Conrad
http://stacks.math.columbia.edu/tag/0AIP#comment-1944

If you can prove a property P for the maps

U \times_X V ---> U \times V

and P is preserved by base change, then P follows for
the diagonal X ---> X \times X. Applying this to
formal algebraic spaces we get a shorter proof of the
basic properties of their diagonals

Whitespace changes

LaTeX: get rid of useless brackets

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.

Started tags infrastructure

	new file:   scripts/add_tags.py
	modified:   scripts/functions.py
	new file:   tags/initial_tags
	new file:   tags/tags

More neurotic changes

Copied over the stuff on Zariski sites to etale and fppf cases

	modified:   categories.tex
	modified:   fpqc-descent.tex
	modified:   spaces.tex
	modified:   topologies.tex