Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalar actions in Lean's mathlib   Scalar actions are ubiquitous in mathematics, and therefore it is valuable to
be able to write them succinctly when formalizing. In this paper we explore how
Lean 3's typeclasses are used by mathlib for scalar actions with examples,
illustrate some of the problems which come up when using them such as
compatibility of actions and non-definitionally-equal diamonds, and note how
these problems can be solved. We outline where more work is needed in mathlib
in this area.

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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex