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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeApr 3rd 2010
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownDoes anyone know how to classify `track extensions' of a category. Baues and Wirsching do the Abelian case, but I have a non-Abelian case, so have a given category C and look for a 2-category C' with \pi_0 being C and in which 2-cells are invertible. (Same objects as C would be preferred.) Typically there should be a link with both non-Abelian group cohomology and the corresponding theory in sheaf theoretic form. Any ideas??? This is relevant for the [[cohomology of a category]] page as at present this is incomplete. Once I understand Baues-Wirsching (!!!!) I will add a bit to it about that theory. (This needs me to understand their `natural systems' and I am not yet sure I do (in fact I'm pretty sure I don't!)

   Does anyone know how to classify `track extensions' of a category. Baues and Wirsching do the Abelian case, but I have a non-Abelian case, so have a given category C and look for a 2-category C' with \pi_0 being C and in which 2-cells are invertible. (Same objects as C would be preferred.) Typically there should be a link with both non-Abelian group cohomology and the corresponding theory in sheaf theoretic form. Any ideas???

   This is relevant for the cohomology of a category page as at present this is incomplete. Once I understand Baues-Wirsching (!!!!) I will add a bit to it about that theory. (This needs me to understand their `natural systems' and I am not yet sure I do (in fact I'm pretty sure I don't!)

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeApr 4th 2010
   • (edited Apr 4th 2010)
   • PermaLink
   Author: zskoda
   Format: MarkdownMamuka Jibladze was indeed explaining me few years ago a viewpoint on track extension as torsors in certain abtract setup, but I do not remember any details. I wish he would be accessible (Mamuka disappeared from mathematical community for a while, while trying his best in his administrative effort to help contribute to the reform of science and education in Republic of Georgia the right way; it is not clear when will this noble administrative burden free him back to the delight of mathematics community). By the way, another useful viewpoint might be from a paper of [[Petar Pavesic|Petar Pavešic]] with a look at the Baues-Wirsching cohomology from the point of view of Grothendieck construction.

   Mamuka Jibladze was indeed explaining me few years ago a viewpoint on track extension as torsors in certain abtract setup, but I do not remember any details. I wish he would be accessible (Mamuka disappeared from mathematical community for a while, while trying his best in his administrative effort to help contribute to the reform of science and education in Republic of Georgia the right way; it is not clear when will this noble administrative burden free him back to the delight of mathematics community).

   By the way, another useful viewpoint might be from a paper of Petar Pavešic with a look at the Baues-Wirsching cohomology from the point of view of Grothendieck construction.

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeApr 5th 2010
   • PermaLink
   Author: Tim_Porter
   Format: Markdown@Zoran: Mamuka did write a paper with Pirashvili in which the torsor viewpoint was discussed. I will have to get a proper copy as I have only seen it on someone else's computer! Thanks for the info.

   @Zoran: Mamuka did write a paper with Pirashvili in which the torsor viewpoint was discussed. I will have to get a proper copy as I have only seen it on someone else's computer! Thanks for the info.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeApr 5th 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownThen just ask Teimuraz about the article. He can still be reached :)

   Then just ask Teimuraz about the article. He can still be reached :)