Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birings and plethories of integer-valued polynomials   Let $A$ and $B$ be commutative rings with identity. An {\it $A$-$B$-biring}
is an $A$-algebra $S$ together with a lift of the functor $Hom_A(S,-)$ from
$A$-algebras to sets to a functor from $A$-algebras to $B$-algebras. An {\it
$A$-plethory} is a monoid object in the monoidal category, equipped with the
composition product, of $A$-$A$-birings. The polynomial ring $A[X]$ is an
initial object in the category of such structures. The $D$-algebra $Int(D)$ has
such a structure if $D = A$ is a domain such that the natural $D$-algebra
homomorphism $\theta_n: {\bigotimes_D}_{i = 1}^n Int(D) \longrightarrow
Int(D^n)$ is an isomorphism for $n = 2$ and injective for $n \leq 4$. This
holds in particular if $\theta_n$ is an isomorphism for all $n$, which in turn
holds, for example, if $D$ is a Krull domain or more generally a TV PVMD. In
these cases we also examine properties of the functor $Hom_D(Int(D),-)$ from
$D$-algebras to $D$-algebras, which we hope to show is a new object worthy of
investigation in the theory of integer-valued polynomials.

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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio