BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Scalars &amp\; probabilities\, monads &amp\; categories - Bart Jac
 obs\, Radboud University Nijmegen\, The Netherlands
DTSTART:20100521T130000Z
DTEND:20100521T140000Z
UID:TALK24545@talks.cam.ac.uk
CONTACT:Sam Staton
DESCRIPTION:The talk consist of two separate but\nconnected parts. The fir
 st part is joint work with\nDion Coumans (Nijmegen). It describes interrel
 atedness between:\n\n# algebraic structure on sets of scalars\,\n# propert
 ies of monads associated with such sets of scalars\, and\n# structure in c
 ategories (esp. Lawvere theories) associated with these monads.\n\nThese i
 nterrelations will be expressed in terms of ``triangles of\nadjunctions''\
 , involving for instance various kinds of monoids\n(non-commutative\, comm
 utative\, involutive) and semirings as\nscalars. It will be shown to which
  kind of monads and categories\nthese algebraic structures correspond via 
 adjunctions.\n\nThe second part will investigate extensions of these resul
 ts\nto probabilities as scalars. It involves convex sets\,\neffect algebra
 s\, and a new class of functors that we call\n`convex functors'\; they inc
 lude what are usually called probablity\ndistribution functors. The relati
 onships take the form of three\nadjunctions. Two of these three are `dual'
  adjunctions for\nconvex sets\, one time with the Boolean truth values {0\
 ,1} as\ndualising object\, and one time with the probablity values\n[0\,1]
  of the unit interval. The third one is a new adjunction\nbetween effect a
 lgebras and convex functors\, forming the first\nstep towards a ``triangle
  of adjunctions'' in this probabilistic area.
LOCATION:Room FW11\, Computer Laboratory\, William Gates Building
END:VEVENT
END:VCALENDAR