Being Van Kampen is a universal property

Details Being Van Kampen is a universal property Being Van Kampen is a universal property

2011-01-24

arxiv.org/abs/1101.4594v2

LMCS 7 (1:14) 2011

Mathematics

Category Theory

22 pages

Scientific paper

10.2168/LMCS-7(1:14)2011

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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