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SUMMARY:Kernels and weak factorisation systems - Richard Garner (Universit
 y of Cambridge)
DTSTART:20100302T141500Z
DTEND:20100302T154500Z
UID:TALK23383@talks.cam.ac.uk
CONTACT:Nathan Bowler
DESCRIPTION:Suppose given a category V which is a suitable base for enrich
 ment. Now for any (weak) factorisation system (L\,R) on V\, and any V-enri
 ched category C\, we may enquire as to whether the former may be lifted "r
 epresentably" to the latter\; in other words\, whether there is a (weak) f
 actorisation system (L'\, R') on C whose right class R' comprises those ma
 ps in C which are sent by each covariant representable to a map in R.\n\nW
 e show that\, under suitable (co)completeness and boundedness assumptions 
 on the category C\, our question may be answered in the affirmative\; the 
 heart of the matter being a (possibly iterated) generalised kernel-cokerne
 l construction.\n
LOCATION:MR9\, Centre for Mathematical Sciences
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