Re: Limits in REL

REL has very few limits other than biproducts: it doesn't even have splittings for all idempotents (so no equalizers or coequalizers). The simplest non-splittable idempotent is the usual order relation on {0,1}, and the same example works in REL(C) for any regular C where the disjoint coproduct 1+1 exists. Peter Johnstone On Thu, 3 Jul 2014, Ondrej Rypacek wrote:

Hi all

What is known about limits in REL , the (bi)category of sets and relations? I know there are biproducts; are there equalisers?

And what about SPAN(C) or REL(C), spans and relations over a suitable category C ?

Thanks a lot in advance, Ondrej

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