Pawel Sobocinski ; Tobias Heindel - Being Van Kampen is a universal property

lmcs:701 - Logical Methods in Computer Science, April 1, 2011, Volume 7, Issue 1 - https://doi.org/10.2168/LMCS-7(1:14)2011
Being Van Kampen is a universal propertyArticle

Authors: Pawel Sobocinski ORCID; Tobias Heindel

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.

Comment: 22 pages

https://doi.org/10.2168/LMCS-7(1:14)2011
Source: arXiv.org:1101.4594
Volume: Volume 7, Issue 1
Secondary volumes: Selected Papers of the 3rd Conference on Algebra and Coalgebra in Computer Science (CALCO 2009)
Published on: April 1, 2011
Imported on: October 19, 2010
Keywords: Mathematics - Category Theory, Computer Science - Programming Languages, cs.PL
Licence: arXiv.org - Non-exclusive license to distribute

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