Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Geometry of Holmsen's Combinatorial Version of the Colorful
  Carath\'eodory   Carath\'eodorys Theorem of convex hulls plays an important role in convex
geometry. In 1982, B\'ar\'any formulated and proved a more general version,
called the Colorful Carath\'eodory. This colorful version was even more
generalized by Holmsen in 2016. He formulated a combinatorial extension and
found a topological proof. Taking a dual point of view we gain an equivalent
formulation of Holmsen's result that has a more geometric meaning.

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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph