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CATEGORIES:Junior Algebra/Logic/Number Theory seminar
SUMMARY:An Introduction to Classifying Toposes - Guilherme
Frederico Lima de Carvalho e Silva (University of
Cambridge)
DTSTART;TZID=Europe/London:20111014T140000
DTEND;TZID=Europe/London:20111014T150000
UID:TALK33721AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/33721
DESCRIPTION:The canonical place to interpret a first-order the
ory is the category of sets considering the well-b
ehaved interaction between the syntax of the theor
y and the semantics that it provides. For more gen
eral theories (e.g. infinitary ones) this interact
ion is not so well-behaved\, but by working in a m
ore general setting we may find a suitable general
ised universe of sets\, i.e. a topos\, where analo
gous interactions may be found. Thus Topos Theory
can be thought of as a generalised Model Theory\,
where the classifying topos of a theory generalise
s the role that the category of sets plays for fir
st-order theories.\n\nI will assume the audience i
s familiar with the notions of adjunction and cate
gorical limit\, and will focus at least half of th
e talk on introducing the notion of topos along wi
th many examples since this material shall serve a
s pre-requisite for many of the other talks given
by the Category Theory group.
LOCATION:MR4
CONTACT:Jonathan Nelson
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