Pawel, Sobocinski and Heindel, Tobias
Being Van Kampen is a universal property
Logical Methods in Computer Science, 7, (1), . (doi:10.2168/LMCS-7(1:14)2011).
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Colimits that satisfy the Van Kampen condition have interesting exactness properties. We show that the elementary presentation of the Van Kampen condition is actually a characterisation of a universal property in the associated bicategory of spans. The main theorem states that Van Kampen cocones are precisely those diagrams in a category that induce bicolimit diagrams in its associated bicategory of spans, provided that the category has pullbacks and enough colimits.
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