Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational Paths -- A Weak Groupoid   We use a labelled deduction system based on the concept of computational
paths (sequences of rewrites) as equalities between two terms of the same type.
We also define a term rewriting system that is used to make computations
between these computational paths, establishing equalities between equalities.
We use a labelled deduction system based on the concept of computational paths
(sequences of rewrites) as our tool, to perform in algebraic topology an
approach of computational paths. This makes it possible to build the
fundamental groupoid of a type $X$ connected by paths. Then, we will establish
the morphism between these groupoid structures, getting the concept of
isomorphisms between types and to constitute the category of computational
paths, which will be called $\mathcal{C}_{paths}$. Finally, we will conclude
that the weak category $\mathcal{C}_{paths}$ determines a weak groupid.

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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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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: econ
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: nlin