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SUMMARY:Dagger limits - Martti Karvonen (University of Edinburgh)
DTSTART:20180918T131500Z
DTEND:20180918T141500Z
UID:TALK109927@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:A dagger category is a category equipped with a dagger: a cont
 ravariant involutive identity-on-objects endofunctor. Such categories are 
 used to model quantum computing and reversible computing\, amongst others.
  The philosophy when working with dagger categories is that all structure 
 in sight should cooperate with the dagger. This causes dagger category the
 ory to differ in many ways from ordinary category theory. Standard theorem
 s have dagger analogues once one figures out what "cooperation with the da
 gger" means for each concept\, but often this is not just an application o
 f formal 2-categorical machinery or a passage to (co)free dagger categorie
 s.\nWe discuss limits in dagger categories. To cooperate with the dagger\,
  limits in dagger categories should be defined up to an unique unitary (in
 stead of only up to iso)\, that is\, an isomorphism whose inverse is its d
 agger. We exhibit a definition that achieves this and generalises known ca
 ses of dagger limits. Moreover\, we discuss connections to polar decomposi
 tion\, applications to ordinary category theory and time permitting\, addr
 ess commutativity of dagger limits with dagger colimits.
LOCATION:MR4\, Centre for Mathematical Sciences
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