Geodesic
Localization, Algebraic Loops and H-Spaces II
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 812-817

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In a previous work [6] it was shown that by imposing certain finiteness conditions on a nilpotent loop certain algebraic results yielded properties about [X, Y] where X is finite CW and Y is an H-Space. In this sequel we further restrict the category of nilpotent loops to a full subcategory called H-loops which still contains all loops of the form [X, Y], We prove that on this category there is a unique and universal P-localization if P ≠ ∅ which corresponds to topological localization. We also show that if the H-loop is a group then the two concepts of localization agree.The first section of this paper is devoted to the definition and basic properties of H-loops. In the second section we develop the localization construction and prove uniqueness. Finally, in the third section we consider the topological and group theoretic situations. 
Shar, Albert O. Localization, Algebraic Loops and H-Spaces II. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 812-817. doi: 10.4153/CJM-1979-075-x
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