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DTSTART:19700329T010000
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CATEGORIES:Logic and Semantics Seminar (Computer Laboratory)
SUMMARY:Scalars &\; probabilities\, monads &\; categ
ories - Bart Jacobs\, Radboud University Nijmegen\
, The Netherlands
DTSTART;TZID=Europe/London:20100521T140000
DTEND;TZID=Europe/London:20100521T150000
UID:TALK24545AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/24545
DESCRIPTION:The talk consist of two separate but\nconnected pa
rts. The first part is joint work with\nDion Couma
ns (Nijmegen). It describes interrelatedness betwe
en:\n\n# algebraic structure on sets of scalars\,\
n# properties of monads associated with such sets
of scalars\, and\n# structure in categories (esp.
Lawvere theories) associated with these monads.\n\
nThese interrelations will be expressed in terms o
f ``triangles of\nadjunctions''\, involving for in
stance various kinds of monoids\n(non-commutative\
, commutative\, involutive) and semirings as\nscal
ars. It will be shown to which kind of monads and
categories\nthese algebraic structures correspond
via adjunctions.\n\nThe second part will investiga
te extensions of these results\nto probabilities a
s scalars. It involves convex sets\,\neffect algeb
ras\, and a new class of functors that we call\n`c
onvex functors'\; they include what are usually ca
lled probablity\ndistribution functors. The relati
onships take the form of three\nadjunctions. Two o
f these three are `dual' adjunctions for\nconvex s
ets\, one time with the Boolean truth values {0\,1
} as\ndualising object\, and one time with the pro
bablity values\n[0\,1] of the unit interval. The t
hird one is a new adjunction\nbetween effect algeb
ras and convex functors\, forming the first\nstep
towards a ``triangle of adjunctions'' in this prob
abilistic area.
LOCATION:Room FW11\, Computer Laboratory\, William Gates Bu
ilding
CONTACT:Sam Staton
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