Geodesic
The Homotopy of Simplicial Algebras
Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1411-1422

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

In [6] Walter Taylor investigated the relationship between the algebraic structure of a topological algebra A and the group structure of its fundamental group π1(A) and of the higher homotopy groups πn(A),n > 1. The main result is that a variety satisfies a group law λ in homotopy (that is, π 1) if and only if every group in the idempotent reduct of obeys λ. (The relevant definitions are in [6] and also § 2 of this paper.) A similar result is stated for the higher homotopy groups. As Taylor points out in the introduction, the hard part of the theorem is constructing a topological algebra in whose fundamental group may fail to obey λ; indeed, in [6] this is only done in detail for the commutative law, and the proof is rather computational. 
Lakser, Harry. The Homotopy of Simplicial Algebras. Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1411-1422. doi: 10.4153/CJM-1980-111-6
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