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CATEGORIES:Category Theory Seminar
SUMMARY:Barren structures and badly behaved monads on the
category of sets. - Nathan Bowler\, Hamburg
DTSTART;TZID=Europe/London:20120313T141500
DTEND;TZID=Europe/London:20120313T151500
UID:TALK34891AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/34891
DESCRIPTION:The theory of monads on Set has been hampered by a
lack of good counterexamples - for example\, alth
ough at first it was believed that the continuatio
ns monad might be nasty enough that there would be
some monad with which it would have no tensor pro
duct\, it was shown by Goncharov and Schroeder tha
t this monad is uniform\, and so it does have tens
or products with all other monads on Set. There is
a serious lack of examples of non-uniform monads\
, though one such monad (the wellorder monad) has
been examined and shown to have no tensor product
with the nonempty list monad.\n\nI'll present a ne
w technique for building badly behaved monads on S
et\, by making use of large algebraic structures w
hich don't have small generating sets (I'll call s
uch structures barren). I'll use this technique to
show how a couple of interesting counterexamples
can be built: a monad with no tensor product with
the finite power set monad\, and an N-indexed sequ
ence of monads whose colimit is universe-dependent
.
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Julia Goedecke
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