Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructive sheaf models of type theory   We generalise sheaf models of intuitionistic logic to univalent type theory
over a small category with a Grothendieck topology. We use in a crucial way
that we have constructive models of univalence, that can then be relativized to
any presheaf models, and these sheaf models are obtained by localisation for a
left exact modality. We provide first an abstract notion of descent data which
can be thought of as a higher version of the notion of prenucleus on frames,
from which can be generated a nucleus (left exact modality) by transfinite
iteration. We then provide several examples.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph