BEGIN:VCALENDAR VERSION:2.0 PRODID:-// 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:TALK48602AT URL: 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