Being Van Kampen is a universal property
Category Theory
2015-07-01 v2 Programming Languages
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.
Cite
@article{arxiv.1101.4594,
title = {Being Van Kampen is a universal property},
author = {Pawel Sobocinski and Tobias Heindel},
journal= {arXiv preprint arXiv:1101.4594},
year = {2015}
}
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22 pages