Applied Categorical Structures

, Volume 11, Issue 3, pp 287–312 | Cite as

On Colimits in Categories of Relations

  • Stefan Milius


We study (finite) coproducts and colimits of ω-chains in Rel(C), the 2-category of relations over a given category C. The former exist and are “the same” as in C provided that C is extensive. The latter do not exist for example in Rel(Set). However, the canonical construction of those colimits in the category of sets can be generalized to Rel(Set). The canonical cocone is shown to satisfy a 2-categorical universal property, namely that of an lax adjoint cooplimit. Sufficient conditions for any base category C to admit the construction are given.

A necessary and sufficient condition for the construction to yield colimits of ω-chains in the category of maps of Rel(C) is also given.

relation map (co)limit of ω-chains (co)products 2-categories initial algebra construction 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Stefan Milius
    • 1
  1. 1.Institute of Theoretical Computer ScienceTechnical UniversityBraunschweigGermany

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