Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Triples, Operads, and Generalized Homogeneous Functors   We study the splitting of the Goodwillie towers of functors in various
settings. In particular, we produce splitting criteria for functors $F: \A \to
M_A$ from a pointed category with coproducts to $A$-modules in terms of
differentials of $F$. Here $A$ is a commutative $S$-algebra. We specialize to
the case when $\A$ is the category of $\a$-algebras for an operad $\a$ and $F$
is the forgetful functor, and derive milder splitting conditions in terms of
the derivative of $F$. In addition, we describe how triples induce operads, and
prove that, roughly speaking, a triple $T$ is naturally equivalent to the
product of its Goodwillie layers if and only if it is an algebra over its
induced operad.

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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: cs
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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: cond-mat