Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the perturbation algebra   We introduce a certain differential graded bialgebra, neither commutative nor
cocommutative, that governs perturbations of a differential on complexes
supplied with an abstract Hodge decomposition. This leads to a conceptual
treatment of the Homological Perturbation Lemma and its multiplicative version.
As an application we give an explicit form of the decomposition theorem for
$A_\infty$ algebras and $A_\infty$ modules and, more generally, for twisted
objects in differential graded categories.

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
19
The categories of this paper are: eess