Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Univalent categories and the Rezk completion   We develop category theory within Univalent Foundations, which is a
foundational system for mathematics based on a homotopical interpretation of
dependent type theory. In this system, we propose a definition of "category"
for which equality and equivalence of categories agree. Such categories satisfy
a version of the Univalence Axiom, saying that the type of isomorphisms between
any two objects is equivalent to the identity type between these objects; we
call them "saturated" or "univalent" categories. Moreover, we show that any
category is weakly equivalent to a univalent one in a universal way. In
homotopical and higher-categorical semantics, this construction corresponds to
a truncated version of the Rezk completion for Segal spaces, and also to the
stack completion of a prestack.

25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex