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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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