Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A binary operation on the class of coherently diagonal complexes   We use mathematical induction to prove that the horizontal composition in the
class of coherently diagonal complexes is indeed a binary operation. That is to
say, the embedding of two coherently diagonal complexes in an alternating
planar diagram produces a coherently diagonal complex.

1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga