The interpretation by Duskin and Glenn of abelian sheaf cohomology as connected components of a category of torsors is extended to homotopy classes. This is simultaneously an extension of Verdier's version of Cech cohomology to homotopy.
Theory and Applications of Categories, Vol. 9, 2001, No. 3, pp 43-60 http://www.tac.mta.ca/tac/volumes/9/n3/n3.dvi http://www.tac.mta.ca/tac/volumes/9/n3/n3.ps http://www.tac.mta.ca/tac/volumes/9/n3/n3.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/9/n3/n3.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/9/n3/n3.psTAC Home