The Stacks project

Fix equation in algebra

Thanks to T.C.
https://stacks.math.columbia.edu/tag/00DD#comment-7380

Fix a second proof in algebra

Thanks to Shota Inoue
https://stacks.math.columbia.edu/tag/00DD#comment-5989

More standard use of "partial ordering"

Thanks to Wei Xu
http://stacks.math.columbia.edu/tag/00CR#comment-588
and to Keenan Kidwell
http://stacks.math.columbia.edu/tag/00D3#comment-2102

Invisible changes

Part of neurotically trying to uniformize use of latex commands in math
mode.

Get rid of \begin{align}

Any equation which is numbered should have a label and this should only
happen for equation environments

Fixes for material flat modules

Thanks to remarks by Fan on the site, especially
http://stacks.math.columbia.edu/tag/00HD#comment-396

Add section on colimits to algebra.tex

Whitespace changes

LaTeX: get rid of useless brackets

LaTeX: uniformize notation

LaTeX: fix colim

	Introduced the macro

	\def\colim{\mathop{\rm colim}\nolimits}

	and changed all the occurences of \text{colim} into \colim.

Code changes only

	Changes to algebra,tex which have no effect on the produced pdf
	files.

Started tags infrastructure

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

List of changes:
	Improved exposition colimits modules in algebra.tex
	Fixed typo on categories.tex
	Proof basic lemma cohomology P^n_R, R Noetherian
	Characterize affines by vanishing cohomology
	Cohmology commutes with directed colimits sometimes
	Typos constructions.tex
	Clarify quasi-affine section
	Ideals directed limit finite type ideals
	Characterize affines in properties.tex
	Closed points exist in quasi-compact spaces

	modified:   algebra.tex
	modified:   categories.tex
	modified:   coherent.tex
	modified:   cohomology.tex
	modified:   constructions.tex
	modified:   limits.tex
	modified:   modules.tex
	modified:   properties.tex
	modified:   topology.tex

More neurotic changes

More neurotic changes

Neurotic changes continued

	modified:   algebra.tex
	modified:   constructions.tex
	new file:   scripts/commands.py
	modified:   scripts/functions.py
	modified:   simplicial.tex

There are a lot of mistakes in this commit

	modified:   algebra.tex
	modified:   categories.tex
	modified:   schemes.tex
	modified:   sheaves.tex
	modified:   sites.tex

Added section on tensor product by Fraser Hiu

	modified:   CONTRIBUTORS
	modified:   algebra.tex