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SUMMARY:Orthogonality and Factorization Systems - Sean Moss (DPMMS)
DTSTART:20131024T130000Z
DTEND:20131024T140000Z
UID:TALK48602@talks.cam.ac.uk
CONTACT:Guilherme Lima de Carvalho e Silva
DESCRIPTION:A basic definition of a factorization system on a category cou
 ld be a pair (E\,M) of classes of morphisms such that every morphism in th
 e category factorizes as the composite of something from E followed by som
 ething from M. For example\, the (epi\,mono)-factorization in the category
  of sets arises from expressing a function as the composite of 'surjection
  onto image' followed by 'inclusion of image into codomain'. (See also Q4 
 CT Sheet 1). Note that in these cases\, the factorizations of a given morp
 hism are (essentially) unique.\n\nOrthogonality is a simple binary relatio
 n on the morphisms of a category\, which will allow us to define the notio
 n of an 'Orthogonal Factorization System' (OFS). I will justify the defini
 tion by showing that it is (almost) equivalent to 'factorization system wi
 th unique factorizations' and go on to describe the basic properties and e
 xamples of OFS's. I hope to explain the connection to reflective subcatego
 ries and the orthogonal subcategory problem and talk about some existence 
 theorems.
LOCATION:CMS\, MR13
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