Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unifying cubical and multimodal type theory   In this paper we combine the principled approach to programming with
modalities of multimodal type theory (MTT) with the computationally
well-behaved identity types of cubical type theory (CTT). The result -- cubical
modal type theory (Cubical MTT) -- has the desirable features of both systems.
In fact, the whole is more than the sum of its parts: Cubical MTT validates
desirable extensionality principles for modalities that MTT only supported
through ad hoc means.
  We investigate the semantics of Cubical MTT and provide an axiomatic approach
to producing models of Cubical MTT based on the internal language of topoi and
use it to construct presheaf models. Finally, we demonstrate the practicality
and utility of this axiomatic approach to models by constructing a model of
(cubical) guarded recursion in a cubical version of the topos of trees. We then
use this model to justify an axiomatization of Lob induction and thereby use
Cubical MTT to smoothly reason about guarded recursion.

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The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn