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SUMMARY:Constructive conceptual completeness for regular logic - Panagis K
 arazeris (University of Patras)
DTSTART:20160112T141500Z
DTEND:20160112T151500Z
UID:TALK63328@talks.cam.ac.uk
CONTACT:Zhen Lin Low
DESCRIPTION:Conceptual completeness for coherent categories (due to M. Mak
 kai and G. Reyes) says that if a coherent functor F: C → D induces an eq
 uivalence COH(D\, Set) → COH(C\, Set) between their categories of Set-va
 lued models\, then the induced functor P(F): P(C) → P(D) between the ass
 ociated pretoposes is an equivalence. Their arguments are model-theoretic 
 (involving compactness and the method of diagrams). Later A. Pitts gave a 
 constructive version of that theorem\, allowing models in (an adequate cla
 ss of) toposes (and relaxing the notion of equivalence to mean fully faith
 ful and essentially surjective on objects).  A similar result by Makkai fo
 r regular logic says that if a regular functor F: C → D induces an equiv
 alence REG(D\, Set) → REG(C\, Set)\, then the induced E(F): E(C) → E(D
 ) between the respective effectivizations of the regular categories is an 
 equivalence. The latter comes as a corollary to a more general duality res
 ult of his that\, again\, uses model-theoretic methods. We exploit the res
 ult of Pitts\, along with a (seemingly) hitherto unnoticed property of eff
 ectivization\, to give a direct and constructive proof of that result of M
 akkai.
LOCATION:MR4\, Centre for Mathematical Sciences
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