Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cobordism model for Waldhausen $K$-theory   We study a categorical construction called the cobordism category, which
associates to each Waldhausen category a simplicial category of cospans. We
prove that this construction is homotopy equivalent to Waldhausen's
$S_{\bullet}$-construction and therefore it defines a model for Waldhausen
$K$-theory. As an example, we discuss this model for $A$-theory and show that
the cobordism category of homotopy finite spaces has the homotopy type of
Waldhausen's $A(*)$. We also review the canonical map from the cobordism
category of manifolds to $A$-theory from this viewpoint.

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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio