The Stacks project

Typo in cohomology

Thanks to Laurent Moret-Bailly
https://stacks.math.columbia.edu/tag/01FF#comment-5968

Fix signs in section on Cech cohomology of complexes

	The Cech complex of a complex of abelian sheaves F^* has terms

		C^p(U, F^q)

	and p is the first index. Hence the differential, according to
	our general conventions should be

		Cech differential + sign * differential of F^*

	This simplifies many of the calculations. We also added a script
	which checks the signs for the cup-product.

Cohomology and colimits

	The case of sheaves on sites

Whitespace changes

LaTeX: fix colim

	Introduced the macro

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

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

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