Geodesic
On the Criterion of Stasheff
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 250-255

Voir la notice de l'article provenant de la source Cambridge University Press

In (9), Stasheff showed that a loop space ΩX is homotopy-commutative if and only if the map e∇ : ΣΩX ∨ ΣΩX → X may be extended to ΣΩX × ΣΩX, where ∇ is the folding map and e:ΣΩX → X is the map whose adjoint is the identity map of ΩX. In (5), Ganea, Hilton, and Peterson showed that this criterion does not dualize. Our aim in this paper is to give a reformulation of Stasheff's criterion, which is equivalent to it, but in a form which does dualize. In the course of the paper, we shall discuss why Stasheff's criterion, in its original form, does not dualize. In (5), the authors have, of course, given an explicit counterexample to the dual of StashefFs criterion in its original form. 
On the Criterion of Stasheff. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 250-255. doi: 10.4153/CJM-1969-024-6
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