Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cone of functionals on the Cuntz semigroup   The functionals on an ordered semigroup S in the category Cu--a category to
which the Cuntz semigroup of a C*-algebra naturally belongs--are investigated.
After appending a new axiom to the category Cu, it is shown that the
"realification" S_R of S has the same functionals as S and, moreover, is
recovered functorially from the cone of functionals of S. Furthermore, if S has
a weak Riesz decomposition property, then S_R has refinement and interpolation
properties which imply that the cone of functionals on S is a complete
distributive lattice. These results apply to the Cuntz semigroup of a
C*-algebra. At the level of C*-algebras, the operation of realification is
matched by tensoring with a certain stably projectionless C*-algebra.

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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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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: supr-con
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nlin