Dimension of a stack

I would like to add the notion of dimension of an algebraic stack
to the Stacks Project. At least, I can't find the definition there,
and I think it is really basic and convenient. Once the definition
is there, one could mention the dimension of various stacks
that come up as examples in the Stacks Project.

I attach a Latex file with a proposed write-up of the dimension of a
locally Noetherian stack, following Laumon and Moret-Bailly,
equations 11.14 (definition of dimension of a stack at a point)
and 11.15 (definition of dimension of a stack).
I had to prepare some ground about schemes and algebraic spaces first.
So the attached file
is intended to be divided into three parts: (1) add to the end of the
section "Smooth morphisms" in the chapter
"Morphisms of Schemes";
(2) add to the end of the section "Smooth morphisms" in the chapter
"Morphisms of Algebraic Spaces";
and (3) a new section for the chapter "Properties of Algebraic Stacks".

I tried to label the way my file is divided into three parts.

I hope you can use this for the Stacks Project.

Best wishes,
Burt
Generalize lemma on dimension and smooth morphisms

The case of schemes
Generalize lemma on dimension and smooth morphisms

The case of algebraic spaces
Spell out why dimension is well defined

This is kind of annoying and at the moment only works for locally
Noetherian stacks.
Fix some snafus found by scripts
Tags: added new tags