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SUMMARY:Characterizing weakly Schreier extensions of monoids  - Peter Faul
  (University of Cambridge)
DTSTART:20200204T141500Z
DTEND:20200204T151500Z
UID:TALK139270@talks.cam.ac.uk
CONTACT:José Siqueira
DESCRIPTION:It is well known that split extensions of groups H by N corres
 pond to actions of H on N. This is not so for monoids\, however actions of
  monoids do correspond to a certain class of split extensions\, called the
  Schreier extensions. A split extension comprising kernel k: N -> G\, coke
 rnel e: G -> H and splitting s: H -> G is said to be Schreier when for eac
 h g in G\, there is a unique n in N and h in H such that g = k(n)s(h). The
  uniqueness condition can be relaxed providing the notion of a weakly Schr
 eier extension\, of which the Artin glueings of topological spaces provide
  a natural example. \n\nIn this talk we provide a characterization of weak
 ly Schreier extensions between monoids N and H\, as a certain quotient of 
 N x H\, paired with something that resembles an action. We then use this c
 haracterization to construct some new examples of weakly Schreier extensio
 ns.
LOCATION:MR4\, Centre for Mathematical Sciences
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