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Kernels and weak factorisation systems

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If you have a question about this talk, please contact Nathan Bowler.

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.

This talk is part of the Category Theory Seminar series.

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