Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The identity type weak factorisation system   We show that the classifying category C(T) of a dependent type theory T with
axioms for identity types admits a non-trivial weak factorisation system. We
provide an explicit characterisation of the elements of both the left class and
the right class of the weak factorisation system. This characterisation is
applied to relate identity types and the homotopy theory of groupoids.

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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex