Dear Ondrej, Since many people have already replied to you about Rel, let me add something about colimits in Span(C). Note that since Span(C) is a bicategory, the "morally correct" notion is bicolimits. With Tobias Heindel we showed that any colimit diagram in C that satisfies something called a Van Kampen property is mapped to a bicolimit diagram through the canonical embedding C -> Span(C). So the Van Kampen property is really a characterisation of when a colimit satisfies the universal property of being a (bi)colimit in the wild world of Span(C). Some examples of Van Kampen properties for particular colimits: a Van Kampen initial object is a strict initial object, a Van Kampen coproduct is a coproduct that has the properties of coproducts in extensive categories, a Van Kampen pushout is a pushout that has the properties of pushouts (along monos) in adhesive categories. You will find the details and more examples in: Tobias Heindel, Pawel Sobocinski: Being Van Kampen is a universal property. Logical Methods in Computer Science 7(1) (2011) All the best, Pawel. On 3 July 2014 11:57, Ondrej Rypacek <ondrej.rypacek@gmail.com> 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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