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CATEGORIES:Category Theory Seminar
SUMMARY:Constructive conceptual completeness for regular l
ogic - Panagis Karazeris (University of Patras)
DTSTART;TZID=Europe/London:20160112T141500
DTEND;TZID=Europe/London:20160112T151500
UID:TALK63328AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/63328
DESCRIPTION:Conceptual completeness for coherent categories (d
ue to M. Makkai and G. Reyes) says that if a coher
ent functor F: C → D induces an equivalence COH(D\
, Set) → COH(C\, Set) between their categories of
Set-valued models\, then the induced functor P(F):
P(C) → P(D) between the associated pretoposes is
an equivalence. Their arguments are model-theoreti
c (involving compactness and the method of diagram
s). Later A. Pitts gave a constructive version of
that theorem\, allowing models in (an adequate cla
ss of) toposes (and relaxing the notion of equival
ence to mean fully faithful and essentially surjec
tive on objects). A similar result by Makkai for
regular logic says that if a regular functor F: C
→ D induces an equivalence REG(D\, Set) → REG(C\,
Set)\, then the induced E(F): E(C) → E(D) between
the respective effectivizations of the regular cat
egories is an equivalence. The latter comes as a c
orollary to a more general duality result of his t
hat\, again\, uses model-theoretic methods. We exp
loit the result of Pitts\, along with a (seemingly
) hitherto unnoticed property of effectivization\,
to give a direct and constructive proof of that r
esult of Makkai.
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:Zhen Lin Low
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