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SUMMARY:An introduction to the theory of derivators
DTSTART:20121116T141500
DTEND:20121116T153000
DTSTAMP:20260427T134112Z
UID:0a82a9e933cffeb02776e46282dd463a334e35f22ba43c623ed7ce96
CATEGORIES:Conferences - Seminars
DESCRIPTION:Moritz Groth (Nijmegen)\nThe theory of derivators --going back
  to Grothendieck and Heller-- is a purely (2-)categorical approach to axio
 matic homotopy theory. It adresses the problem that the rather crude passa
 ge from model categories to homotopy categories results in a serious loss 
 of information. In the stable context\, the typical defects of triangulate
 d categories (non-functoriality of cone construction\, lack of homotopy co
 limits) can be seen as a reminiscent of this fact.\n\nThe basic idea behin
 d a derivator is that it forms homotopy categories of 'all' diagram catego
 ries and also encodes the calculus of homotopy Kan extensions.\n\nThe aim 
 of this talk is to give an introduction to derivators and to (hopefully) a
 dvertise them as a convenient\, 'weakly terminal' approach to axiomatic ho
 motopy theory. We will see that there is a threefold hierarchy of such str
 uctures\, namely derivators\, pointed derivators\, and stable derivators. 
 A nice fact about this theory is that 'stability' is a property of a deriv
 ator as opposed to being an additional structure.
LOCATION:MA 10
STATUS:CONFIRMED
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