BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Junior Category Theory Seminar
SUMMARY:Orthogonality and Factorization Systems - Sean Mos
s (DPMMS)
DTSTART;TZID=Europe/London:20131024T140000
DTEND;TZID=Europe/London:20131024T150000
UID:TALK48602AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48602
DESCRIPTION:A basic definition of a factorization system on a
category could be a pair (E\,M) of classes of morp
hisms such that every morphism in the category fac
torizes as the composite of something from E follo
wed by something from M. For example\, the (epi\,m
ono)-factorization in the category of sets arises
from expressing a function as the composite of 'su
rjection onto image' followed by 'inclusion of ima
ge into codomain'. (See also Q4 CT Sheet 1). Note
that in these cases\, the factorizations of a give
n morphism are (essentially) unique.\n\nOrthogonal
ity is a simple binary relation on the morphisms o
f a category\, which will allow us to define the n
otion of an 'Orthogonal Factorization System' (OFS
). I will justify the definition by showing that i
t is (almost) equivalent to 'factorization system
with unique factorizations' and go on to describe
the basic properties and examples of OFS's. I hope
to explain the connection to reflective subcatego
ries and the orthogonal subcategory problem and ta
lk about some existence theorems.
LOCATION:CMS\, MR13
CONTACT:Guilherme Lima de Carvalho e Silva
END:VEVENT
END:VCALENDAR