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arXiv · 1101.4594

Being Van Kampen is a universal property

Pawel Sobocinski·Tobias Heindel
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Abstract

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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Pawel Sobocinski, Tobias Heindel. 2011-01-24. Being Van Kampen is a universal property. https://doi.org/10.2168/lmcs-7(1%3A14)2011

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