Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Peetre-Slov\'ak's theorem revisited   In 1960, J. Peetre proved the finiteness of the order of linear local
operators. Later on, J. Slov\'{a}k vastly generalized this theorem, proving the
finiteness of the order of a broad class of (non-linear) local operators.
  In this paper, we use the language of sheaves and ringed spaces to prove a
simpler version of Slov\'{a}k's result. The statement we prove, adapting
Slov\'{a}k's original ideas, deals with local operators defined between the
sheaves of smooth sections of fibre bundles, and thus covers many of the
applications of Slov\'{a}k's theorem.

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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol