BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Symmetric monoidal closed categories relative to a base - Rory Luc
 yshyn-Wright
DTSTART:20141028T141500Z
DTEND:20141028T153000Z
UID:TALK55861@talks.cam.ac.uk
CONTACT:Dr Ignacio Lopez Franco
DESCRIPTION:If M and V are symmetric monoidal closed categories\, then M m
 ay carry\nan enrichment in V\, but we show that such an enrichment is esse
 ntially\nthe same as a normal morphism M --> V.  We make this precise as a
 n\nequivalence of 2-categories.  Next\, we show that this equivalence\nlif
 ts to an equivalence between 2-categories whose objects are\,\nrespectivel
 y\, (1) tensored symmetric monoidal closed V-categories and\n(2) symmetric
  monoidal closed adjunctions with right adjoint valued in\nV.  Further\, w
 hereas every normal closed functor carries an\nenrichment\, we show also t
 hat (1) and (2) are equivalent to a third\n2-category whose objects are ad
 junctions F -| G : M --> V in the\n2-category of symmetric monoidal closed
  V-categories.  Along the way\,\nwe study change of base for symmetric mon
 oidal V-categories\, and we\nshow that the assignment to each symmetric mo
 noidal closed functor its\nassociated enriched functor is part of a 2-func
 tor valued in an\nop-fibred 2-category of enriched symmetric monoidal clos
 ed categories.
LOCATION:MR5\, Centre for Mathematical Sciences
END:VEVENT
END:VCALENDAR