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SUMMARY:Model structures and derived functors\, minus homotopy - Zhen Lin 
 Low - DPMMS
DTSTART:20131114T140000Z
DTEND:20131114T150000Z
UID:TALK48906@talks.cam.ac.uk
CONTACT:Guilherme Lima de Carvalho e Silva
DESCRIPTION:It is now understood that Quillen’s notion of ‘closed mode
 l category’ captures the essence of abstract homotopy theory very well\;
  but at the same time\, the requirement that model categories have all fin
 ite limits and colimits means that not every (∞\, 1)-category can be pre
 sented by a model category. By relaxing this requirement\, we are able to 
 expand the class of model categories enough to include presentations for a
 ll (∞\, 1)-categories. One curious feature of this development is the ab
 sence of homotopical concepts in the proofs: the basic theory is purely ca
 tegory-theoretic.\n\nExamples in this talk will be drawn from classical ho
 mological algebra. Time permitting\, we will see how Tor and Ext can be de
 scribed as absolute Kan extensions.
LOCATION:CMS\, MR13
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