Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On Nontrivial Weak Dicomplementations and the Lattice Congruences that
  Preserve Them
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an