Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Every 1D Persistence Module is a Restriction of Some Indecomposable 2D
  Persistence Module   A recent work by Lesnick and Wright proposed a visualisation of $2$D
persistence modules by using their restrictions onto lines, giving a family of
$1$D persistence modules. We give a constructive proof that any $1$D
persistence module with finite support can be found as a restriction of some
indecomposable $2$D persistence module with finite support. As consequences of
our construction, we are able to exhibit indecomposable $2$D persistence
modules whose support has holes as well as an indecomposable $2$D persistence
module containing all $1$D persistence modules with finite support as line
restrictions. Finally, we also show that any finite-rectangle-decomposable $n$D
persistence module can be found as a restriction of some indecomposable
$(n+1)$D persistence module.

6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph