Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization in Homotopy Type Theory   We study localization at a prime in homotopy type theory, using self maps of
the circle. Our main result is that for a pointed, simply connected type $X$,
the natural map $X \to X_{(p)}$ induces algebraic localizations on all homotopy
groups. In order to prove this, we further develop the theory of reflective
subuniverses. In particular, we show that for any reflective subuniverse $L$,
the subuniverse of $L$-separated types is again a reflective subuniverse, which
we call $L'$. Furthermore, we prove results establishing that $L'$ is almost
left exact. We next focus on localization with respect to a map, giving results
on preservation of coproducts and connectivity. We also study how such
localizations interact with other reflective subuniverses and orthogonal
factorization systems. As key steps towards proving the main theorem, we show
that localization at a prime commutes with taking loop spaces for a pointed,
simply connected type, and explicitly describe the localization of an
Eilenberg-Mac Lane space $K(G,n)$ with $G$ abelian. We also include a partial
converse to the main theorem.

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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
15
The categories of this paper are: nucl-ex