Uniqueness of n-fold delooping machines Original Research Article

We give an axiomatic characterization of n-fold delooping constructions that leads to uniqueness theorems for these constructions. Such a result implies that if W and W′ are any two n-fold delooping constructions and X is an En-space, then the n-fold deloopings WX and W′X are weakly homotopy equivalent. In particular, the n-fold delooping constructions of May and Segal are equivalent.