Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cochain operations defining Steenrod $\cup_i$-products in the bar
  construction   The set of cochain multioperations defining Steenrod $\smile_i$-products in
the bar construction is constructed in terms of surjection operad. This
structure extends a Homotopy G-algebra structure which defines just the $\cup $
on the bar construction.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con