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CATEGORIES:Junior Category Theory Seminar
SUMMARY:Model structures and derived functors\, minus homo
topy - Zhen Lin Low - DPMMS
DTSTART;TZID=Europe/London:20131114T140000
DTEND;TZID=Europe/London:20131114T150000
UID:TALK48906AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48906
DESCRIPTION:It is now understood that Quillen’s notion of ‘clo
sed model category’ captures the essence of abstra
ct homotopy theory very well\; but at the same tim
e\, the requirement that model categories have all
finite limits and colimits means that not every (
∞\, 1)-category can be presented by a model catego
ry. By relaxing this requirement\, we are able to
expand the class of model categories enough to inc
lude presentations for all (∞\, 1)-categories. One
curious feature of this development is the absenc
e of homotopical concepts in the proofs: the basic
theory is purely category-theoretic.\n\nExamples
in this talk will be drawn from classical homologi
cal algebra. Time permitting\, we will see how Tor
and Ext can be described as absolute Kan extensio
ns.
LOCATION:CMS\, MR13
CONTACT:Guilherme Lima de Carvalho e Silva
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