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CATEGORIES:Category Theory Seminar
SUMMARY:Dagger limits - Martti Karvonen (University of Edi
 nburgh)
DTSTART;TZID=Europe/London:20180918T141500
DTEND;TZID=Europe/London:20180918T151500
UID:TALK109927AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/109927
DESCRIPTION:A dagger category is a category equipped with a da
 gger: a contravariant involutive identity-on-objec
 ts endofunctor. Such categories are used to model 
 quantum computing and reversible computing\, among
 st others. The philosophy when working with dagger
  categories is that all structure in sight should 
 cooperate with the dagger. This causes dagger cate
 gory theory to differ in many ways from ordinary c
 ategory theory. Standard theorems have dagger anal
 ogues once one figures out what "cooperation with 
 the dagger" means for each concept\, but often thi
 s is not just an application of formal 2-categoric
 al machinery or a passage to (co)free dagger categ
 ories.\nWe discuss limits in dagger categories. To
  cooperate with the dagger\, limits in dagger cate
 gories should be defined up to an unique unitary (
 instead of only up to iso)\, that is\, an isomorph
 ism whose inverse is its dagger. We exhibit a defi
 nition that achieves this and generalises known ca
 ses of dagger limits. Moreover\, we discuss connec
 tions to polar decomposition\, applications to ord
 inary category theory and time permitting\, addres
 s commutativity of dagger limits with dagger colim
 its.
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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