Van Kampen Colimits as Bicolimits in Span

Tobias Heindel, Pawel Sobocinski

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The exactness properties of coproducts in extensive categories and pushouts along monos in adhesive categories have found various applications in theoretical computer science, e.g. in program semantics, data type theory and rewriting. We show that these properties can be understood as a single universal property in the associated bicategory of spans. To this end, we first provide a general notion of Van Kampen cocone that specialises to the above colimits. The main result states that Van Kampen cocones can be characterised as exactly those diagrams in ℂ that induce bicolimit diagrams in the bicategory of spans TeX , provided that ℂ has pullbacks and enough colimits.
Original languageEnglish
Title of host publicationAlgebra and Coalgebra in Computer Science
Subtitle of host publicationThird International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings
PublisherSpringer Berlin Heidelberg
Number of pages15
ISBN (Electronic)978-3-642-03741-2
ISBN (Print)978-3-642-03740-5
Publication statusPublished - 2009


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