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CATEGORIES:Junior Category Theory Seminar
SUMMARY:Van Kampen's Theorem: classic\, directed &\; ge
neralized - Tobias Heindel (University of Edinburg
h)
DTSTART;TZID=Europe/London:20140227T140000
DTEND;TZID=Europe/London:20140227T150000
UID:TALK51168AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51168
DESCRIPTION:The talk will start with a review of the basic def
initions and main ideas of the Seifert-Van Kampen
Theorem\, which states that the fundamental group(
oid) functor preserves certain colimits from the c
ategory of "nice" topological spaces to the catego
ry of group(oid)s. It is much less well-known that
the theorem can be generalized without much compl
ication to directed topological spaces and their f
undamental categories\, using essentially the same
proof. The situation is different for the so-call
ed tautological proof of the Van Kampen Theorem\,
which relies on the equivalence between the fundam
ental groupoid π1(X) and the category of covering
spaces Cov(X) for any "nice" space X. The talk wil
l describe the crucial points of the tautological
proof of the VK theorem and finishes with a discus
sion of its rôle in Brown's generalized Van Kampen
theorems\, which gave rise to the study of adhesi
ve categories.\n
LOCATION:CMS\, MR13
CONTACT:Sean Moss
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