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Richard Garner (University of Cambridge)
Tuesday 02 March 2010, 14:15-15:45
Kernels and weak factorisation systems
- đ¤ Speaker: Richard Garner (University of Cambridge)
- đ Date & Time: Tuesday 02 March 2010, 14:15 - 15:45
- đ Venue: MR9, Centre for Mathematical Sciences
Abstract
Suppose given a category V which is a suitable base for enrichment. Now for any (weak) factorisation system (L,R) on V, and any V-enriched category C, we may enquire as to whether the former may be lifted “representably” to the latter; in other words, whether there is a (weak) factorisation system (L’, R’) on C whose right class R’ comprises those maps in C which are sent by each covariant representable to a map in R.
We 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-cokernel construction.
Series This talk is part of the Category Theory Seminar series.
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