Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lie algebra of the group of bisections   Groupoids provide a more appropriate framework for differential geometry than
principal bundles. Synthetic differential geometry is the avant-garde branch of
differential geometry, in which nilpotent infinitesimals are available in
abundance. The principal objective in this paper is to show within our favorite
framework of synthetic differential geometry that the tangent space of the
group of bisections of a microlinear groupoid at its identity is naturally a
Lie algebra. We give essentially distinct two proofs for its Jacobi identity.

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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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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: supr-con
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The categories of this paper are: dg-ga