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CATEGORIES:Category Theory Seminar
SUMMARY:Characterizing weakly Schreier extensions of monoi
ds - Peter Faul (University of Cambridge)
DTSTART;TZID=Europe/London:20200204T141500
DTEND;TZID=Europe/London:20200204T151500
UID:TALK139270AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/139270
DESCRIPTION:It is well known that split extensions of groups H
by N correspond to actions of H on N. This is not
so for monoids\, however actions of monoids do co
rrespond to a certain class of split extensions\,
called the Schreier extensions. A split extension
comprising kernel k: N -> G\, cokernel e: G -> H a
nd splitting s: H -> G is said to be Schreier when
for each g in G\, there is a unique n in N and h
in H such that g = k(n)s(h). The uniqueness condit
ion can be relaxed providing the notion of a weakl
y Schreier extension\, of which the Artin glueings
of topological spaces provide a natural example.
\n\nIn this talk we provide a characterization of
weakly Schreier extensions between monoids N and H
\, as a certain quotient of N x H\, paired with so
mething that resembles an action. We then use this
characterization to construct some new examples o
f weakly Schreier extensions.
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:JosÃ© Siqueira
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