Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Retractions of H-spaces   Stasheff showed that if a map between H-spaces is an H-map, then the
suspension of the map is extendable to a map between cprojective planes of the
H-spaces. Stahseff also proved the converse under the assumption that the
multiplication of the target space of the map is homotopy associative. We show
by giving an example that the assumption of homotopy associativity of the
multiplication of the target space is necessary to show the converse. We also
show an analogous fact for maps between higher homotopy associative H-spaces.

17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess