The Stacks project

Fix coding style in categories

Some ttypos

THanks to Samuel Tiersma
https://stacks.math.columbia.edu/tag/0032#comment-7528

Clear modifications

I have fixed typos of mathematical symbols, incorrect reference number, a/an-errors, and missing hyphens.

Fix small typos

I fixed some small typos.
Moreover, "mapsto" --> "maps to" for consistency, and inserting "objects" to avoid confusion.

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.

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

Corrections in sets.tex and categories.tex

Thanks to Wouter Zomervrucht

Invisible changes

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

Typos in categories.tex

Thanks to Jean-Pierre Gourdot

Improved handling of limits and colimits

Unfortunately we need more different types of limits and colimits...

Add missing label

New proof of Lemma 0032

Small fix of proof of a lemma

Thanks to Daniel Bergh
http://stacks.math.columbia.edu/tag/0032#comment-309
http://stacks.math.columbia.edu/tag/0032#comment-310

spelling corrections

Whitespace changes

LaTeX: Remove useless brackets

LaTeX: fix colim

	Introduced the macro

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

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

First macro of the project

	This gets rid of all the \nolimits commands following \lim by
	defining

	\def\lim{\mathop{\rm lim}\nolimits}

	in the file preamble.tex. As far as I can tell this is
	equivalent to \lim\nolimits where \lim is the internal command
	of TeX. The dvi files produced before and after this commit are
	identical.

LaTeX: fix lim

	Replaced all the occurences of \text{lim} by \lim or
	\lim\nolimits depending on whether the invocation occured in
	display math or not.

Smorgasbord of changes

	Loose ends:
		algebra: add colimit over almost directed cats
		sites-modules: exactness of g_!
		more-morphisms: exactness of g_!
		spaces-morphisms: closed immersions and sheaves
		spaces-more-morphisms: conormal sheaves
	should be fixed up soon

Latex: get rid of some overfull boxes

	modified:   algebra.tex
	modified:   categories.tex
	modified:   sets.tex
	modified:   sheaves.tex

Started tags infrastructure

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

Comparing directed colimits over index categories and index posets

	modified:   categories.tex