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SUMMARY:An Introduction to Classifying Toposes - Guilherme Frederico Lima 
 de Carvalho e Silva (University of Cambridge)
DTSTART:20111014T130000Z
DTEND:20111014T140000Z
UID:TALK33721@talks.cam.ac.uk
CONTACT:Jonathan Nelson
DESCRIPTION:The canonical place to interpret a first-order theory is the c
 ategory of sets considering the well-behaved interaction between the synta
 x of the theory and the semantics that it provides. For more general theor
 ies (e.g. infinitary ones) this interaction is not so well-behaved\, but b
 y working in a more general setting we may find a suitable generalised uni
 verse of sets\, i.e. a topos\, where analogous interactions may be found. 
 Thus Topos Theory can be thought of as a generalised Model Theory\, where 
 the classifying topos of a theory generalises the role that the category o
 f sets plays for first-order theories.\n\nI will assume the audience is fa
 miliar with the notions of adjunction and categorical limit\, and will foc
 us at least half of the talk on introducing the notion of topos along with
  many examples since this material shall serve as pre-requisite for many o
 f the other talks given by the Category Theory group.
LOCATION:MR4
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