Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cotorsion pairs and a $K$-theory Localization Theorem   We show that a complete hereditary cotorsion pair $(\C,\C^\bot)$ in an exact
category $\E$, together with a subcategory $\Z\subseteq\E$ containing
$\C^\bot$, determines a Waldhausen category structure on the exact category
$\C$, in which $\Z$ is the class of acyclic objects.
  This allows us to prove a new version of Quillen's Localization Theorem,
relating the $K$-theory of exact categories $\A\subseteq\B$ to that of a
cofiber. The novel idea in our approach is that, instead of looking for an
exact quotient category that serves as the cofiber, we produce a Waldhausen
category, constructed through a cotorsion pair. Notably, we do not require $\A$
to be a Serre subcategory, which produces new examples.
  Due to the algebraic nature of our Waldhausen categories, we are able to
recover a version of Quillen's Resolution Theorem, now in a more homotopical
setting that allows for weak equivalences.

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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org