Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cosheaf Representations of Relations and Dowker Complexes   The Dowker complex is an abstract simplicial complex that is constructed from
a binary relation in a straightforward way. Although there are two ways to
perform this construction -- vertices for the complex are either the rows or
the columns of the matrix representing the relation -- the two constructions
are homotopy equivalent. This article shows that the construction of a Dowker
complex from a relation is a non-faithful covariant functor. Furthermore, we
show that this functor can be made faithful by enriching the construction into
a cosheaf on the Dowker complex. The cosheaf can be summarized by an integer
weight function on the Dowker complex that is a complete isomorphism invariant
for the relation. The cosheaf representation of a relation actually embodies
both Dowker complexes, and we construct a duality functor that exchanges the
two complexes. Finally, we explore a different cosheaf that detects the failure
of the Dowker complex itself to be a faithful functor.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci