Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Category theoretic properties of the A. R\'enyi and C. Tsallis entropies   The problem of embedding the Tsallis and R\'{e}nyi entropies in the framework
of category theory and their axiomatic foundation is studied. To this end, we
construct a special category MES related to measured spaces. We prove that both
of the R\'{e}nyi and Tsallis entropies can be imbedded in the formalism of
category theory by proving that the same basic functional that appears in their
definitions, as well as in the associated Lebesgue space norms, has good
algebraic compatibility properties. We prove that this functional is both
additive and multiplicative with respect to the direct product and the disjoint
sum (the coproduct) in the category MES, so it is a natural candidate for the
measure of information or uncertainty. We prove that the category MES can be
extended to monoidal category, both with respect to the direct product as well
as to the coproduct. The basic axioms of the original R\'{e}nyi entropy theory
are generalized and reformulated in the framework of category MES and we prove
that these axioms foresee the existence of an universal exponent having the
same values for all the objects of the category MES. In addition, this
universal exponent is the parameter, which appears in the definition of the
Tsallis and R\'{e}nyi entropies.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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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: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: math