Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On representation categories of $A_\infty$-algebras and
  $A_\infty$-coalgebras   In this paper, we use the language of monads, comonads and Eilenberg-Moore
categories to describe a categorical framework for $A_\infty$-algebras and
$A_\infty$-coalgebras, as well as $A_\infty$-modules and $A_\infty$-comodules
over them respectively. The resulting formalism leads us to investigate
relations between representation categories of $A_\infty$-algebras and
$A_\infty$-coalgebras. In particular, we relate $A_\infty$-comodules and
$A_\infty$-modules by considering a rational pairing between an
$A_\infty$-coalgebra $C$ and an $A_\infty$-algebra $A$. The categorical
framework also motivates us to introduce $A_\infty$-contramodules over an
$A_\infty$-coalgebra $C$.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn