Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Being Van Kampen is a universal property   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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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga