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SUMMARY:Barren structures and badly behaved monads on the category of sets
 . - Nathan Bowler\, Hamburg
DTSTART:20120313T141500Z
DTEND:20120313T151500Z
UID:TALK34891@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:The theory of monads on Set has been hampered by a lack of goo
 d counterexamples - for example\, although at first it was believed that t
 he continuations monad might be nasty enough that there would be some mona
 d with which it would have no tensor product\, it was shown by Goncharov a
 nd Schroeder that this monad is uniform\, and so it does have tensor produ
 cts with all other monads on Set. There is a serious lack of examples of n
 on-uniform monads\, though one such monad (the wellorder monad) has been e
 xamined and shown to have no tensor product with the nonempty list monad.\
 n\nI'll present a new technique for building badly behaved monads on Set\,
  by making use of large algebraic structures which don't have small genera
 ting sets (I'll call such structures barren). I'll use this technique to s
 how 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
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