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SUMMARY:Skew monoidal structure on categories of algebras - Philip Saville
  (University of Cambridge)
DTSTART:20171128T141500Z
DTEND:20171128T151500Z
UID:TALK96256@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:(joint work with M. Fiore)\n\nThere is a long tradition of con
 structing monoidal or closed structure on the category of algebras for a m
 onad that is assumed to be commutative\, monoidal\, cartesian closed\, or 
 similar.  In each case\, one builds a tensor product classifying bilinear 
 maps using a coequalizer.  This approach\, initiated by Linton's descripti
 on of the construction\, has been studied by Kock\, Guitart and others\, w
 hile Seal has recently examined the monodial case in some detail.  In this
  talk we explore these ideas for skew monoidal categories\, viz. suitably 
 directed versions of monoidal categories in which the structural maps are 
 not assumed to be invertible.  I will show that for a strong monad T on a 
 skew monoidal category\, the category of T-algebras acquires a skew monoid
 al structure with a tensor product classifying left-linear maps.  I will t
 hen characterise the monoids for this left-linear monoidal structure as pr
 ecisely the T-monoids of Fiore et al\, and give two constructions for free
  monoids in skew monoidal categories.
LOCATION:MR5\, Centre for Mathematical Sciences
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