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SUMMARY:Topoi\, or not topoi\, that is the question - Ian Orton (Universit
 y of Cambridge)
DTSTART:20160304T110000Z
DTEND:20160304T120000Z
UID:TALK65003@talks.cam.ac.uk
CONTACT:Ian Orton
DESCRIPTION:The concept of an elementary topos can be seen as a generalisa
 tion of the category of sets. Every topos possesses an internal language w
 hich can be used to reason about its objects. By retaining enough structur
 e from the category of sets we get a powerful internal language that allow
 s us to reason in familiar\, "set-like" ways. However\, the internal langu
 age differs from set theories\, such as ZF\, in several ways. In particula
 r\, the law of excluded middle does not (in general) hold inside a topos.\
 n\n*Covering*\n* The definition of a topos\n* Examples of topoi/toposes\n*
  Properties and alternative definitions\n* The internal language of a topo
 s\n* Using the internal language\n\n*Prerequisites*\n* Familiarity with ba
 sic category theory\, particularly the category of sets\n* Familiarity wit
 h the simply typed lambda calculus as the internal language for CCCs. See 
 "here":http://www.cl.cam.ac.uk/teaching/1516/L108/materials.html\, lecture
 s 9-11 for details.
LOCATION:Rainbow Room (FS07)\, Computer Laboratory
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