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The Stacks project

History of tag 06NX

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changed the proof 2011-07-09 2a72fc9
Sheaves on Algebraic Stacks

	New chapter where we discuss sheaves on algebraic stacks. Basic
	material only. Not much there now.

	Also added new tags.
assigned tag 06NX 2011-06-15 2aa1b6c
Tags: Added new tags
changed the label to lemma-stack-in-groupoids-over-stack-in-groupoids 2011-06-07 a4b5308
Gerbe over stack in groupoids

	This is, I think, the correct definition of when a stack in
	groupoids is a gerbe over another stack in groupoids (both over
	the same site of course). It is spelled out completely what this
	means in practice, as well as a nice theoretical description
	in terms of ameliorations as in the previous commit.
changed the statement and the proof 2011-06-07 a4b5308
Gerbe over stack in groupoids

	This is, I think, the correct definition of when a stack in
	groupoids is a gerbe over another stack in groupoids (both over
	the same site of course). It is spelled out completely what this
	means in practice, as well as a nice theoretical description
	in terms of ameliorations as in the previous commit.
created statement with label lemma-stack-over-fibred-in-groupoids in stacks.tex 2011-06-07 fcc2791
Amelioration of maps of cats fibred in groupoids

	If X ---> Y is a 1-morphism of cats fibred in groupoids over a
	category C then there is a replacement of X which is fibred in
	groupoids over Y and equivalent to X. Moreover this has a
	certain uniqueness. See actual text for details.