Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation properties and Schauder decompositions in Lipschitz-free
  spaces   We prove that the Lipschitz-free space over a doubling metric space has the
bounded approximation property. We also show that the Lipschitz-free spaces
over $\ell_1^N$ or $\ell_1$ have monotone finite-dimensional Schauder
decompositions.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph