The Stacks project

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.

Corrections in sets.tex and categories.tex

Thanks to Wouter Zomervrucht

Adding a reference pointing to a more general result

Change definition of connected: require nonempty

Thanks to Burt Totaro

LaTeX: Remove 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.

LaTeX: \Mor

	Introduced a macro

	\def\Mor{\mathop{\rm Mor}\nolimits}

	and replaced all the occurences of \text{Mor} with \Mor.

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.

Tags: Added new tags

Exactness properties p_* where p is a point of a topos