Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Idempotent convexity and algebras for the capacity monad and its
  submonads   Idempotent analogues of convexity are introduced. It is proved that the
category of algebras for the capacity monad in the category of compacta is
isomorphic to the category of $(\max,\min)$-idempotent biconvex compacta and
their biaffine maps. It is also shown that the category of algebras for the
monad of sup-measures ($(\max,\min)$-idempotent measures) is isomorphic to the
category of $(\max,\min)$-idempotent convex compacta and their affine maps.

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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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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: math-ph