Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong discrete Morse theory and simplicial L-S category: A discrete
  version of the Lusternik-Schnirelmann Theorem   We prove a discrete version of the Lusternik-Schnirelmann theorem for
discrete Morse functions and the recently introduced simplicial
Lusternik-Schnirelmann category of a simplicial complex. To accomplish this, a
new notion of critical object of a discrete Morse function is presented, which
generalizes the usual concept of critical simplex (in the sense of R. Forman).
We show that the non-existence of such critical objects guarantees the strong
homotopy equivalence (in the Barmak and Minian's sense) between the
corresponding sublevel complexes. Finally, we establish that the number of
critical objects of a discrete Morse function defined on $K$ is an upper bound
for the non-normalized simplicial Lusternik-Schnirelmann category of $K$.

1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th