The Stacks project

Two typos in formal-defos

Thanks to Mingchen
https://stacks.math.columbia.edu/tag/06IW#comment-7733
https://stacks.math.columbia.edu/tag/06IW#comment-7734

Better explanation smooth deformation categories

Not great but sort of OK

Final in series nuerotic edits

LaTeX

Introduced a macro

\def\Ker{\text{Ker}}

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

Nothing to see here: controlling paragraphs neurotically

Whitespace changes

LaTeX: get rid of useless brackets

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.

Versal formal objects

	Now we've got uniqueness of versal formal object (correct
	statement in the correct generality). This introduces a
	different notion of minimality from before -- one which doesn't
	look at what happens on tangent spaces. The result later is then
	going to be that minimality can be read off from what happens on
	tangent spaces, provided we have (S2).

Versal formal objects

	Now we've got uniqueness of versal formal object (correct
	statement in the correct generality). This introduces a
	different notion of minimality from before -- one which doesn't
	look at what happens on tangent spaces. The result later is then
	going to be that minimality can be read off from what happens on
	tangent spaces, provided we have (S2).

One point functor has a hull

Unstuck!

	We slightly changed (S2) halfway back to where it was before and
	now everything works (sofar).

Schlessinger's conditions

	I changed the condition (S2) because for non predeformation
	categories the condition just wasn't the right one (as far as I
	can tell). This has already been a bit of a bore, but hopefully
	it will not be too bad. In particular, if F is a predeformation
	category then the new condition is equivalent to the old
	condition...

Formal objects

	Added a few trivial proofs.

Cofibered in groupoids

	Formal section with only category theory.

The category C_\Lambda

	This turned out to be quite a bit more interesting than I had
	at first imagined. Can you do this without appealing to the
	naive cotangent complex? I am sure you can, but how much longer
	would it be...? Patches welcome.

Tags: Added new tags

	Due to the new material in the chapter on deformation theory.

Fix references

New chapter on formal deformation theory

	Written by Alex Perry.