Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functors induced by Cauchy extension of C*-algebras   In this paper we give three functors $\mathfrak{P}$, $[\cdot]_K$ and
$\mathfrak{F}$ on the category of C$^\ast$-algebras. The functor $\mathfrak{P}$
assigns to each C$^\ast$-algebra $\mathcal{A}$ a pre-C$^\ast$-algebra
$\mathfrak{P}(\mathcal{A})$ with completion $[\mathcal{A}]_K$. The functor
$[\cdot]_K$ assigns to each C$^\ast$-algebra $\mathcal{A}$ the Cauchy extension
$[\mathcal{A}]_K$ of $\mathcal{A}$ by a non-unital C$^\ast$-algebra
$\mathfrak{F}(\mathcal{A})$. Some properties of these functors are also given.
In particular, we show that the functors $[\cdot]_K$ and $\mathfrak{F}$ are
exact and the functor $\mathfrak{P}$ is normal exact.

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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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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-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg