The Stacks project

Explain why a functor is exact

Thanks to Gabriel Ribeiro
https://stacks.math.columbia.edu/tag/02MS#comment-7092

Fix some typos and a mistake

Thanks to Nuno
http://stacks.math.columbia.edu/tag/08KS#comment-466
http://stacks.math.columbia.edu/tag/05QD#comment-467
http://stacks.math.columbia.edu/tag/05QF#comment-468
http://stacks.math.columbia.edu/tag/02MS#comment-469

LaTeX

Introduced a new macro

\def\Coker{\text{Coker}}

and replaced all occurrences of \text{Coker} by \Coker

LaTeX

Added a new macro

\def\Im{\text{Im}}

and replaced all occurrences of \text{Im} by \Im

LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

and replace all occurrences of \text{Ker} with \Ker

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.

Kernels of localization functors

	It turns out that for a multiplicative system in a additive
	category it is easy to determine the "kernel" of the
	localization functor. This then trickles down all the way to the
	case of the localization of a triangulated category.

	Warning: This commit contains partially unfinished work.

More on localization

	Behaviour with respect to finite limits and colimits. What
	happens when you localize a (pre)additive category, or an
	abelian category. Improved exposition of take quotients of
	abelian categories by Serre subcategories.

New tags added to the project

	modified:   tags/tags

Added Serre subcategories to homology.tex
Lots of edits to intersections.tex

	modified:   homology.tex
	modified:   intersections.tex
	modified:   morphisms.tex
	modified:   my.bib