English

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.

Keywords

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}
}

Comments

22 pages

R2 v1 2026-06-21T17:16:12.685Z