Homotopy limits of triples

Given a triple J on the category of (pointed) spaces, one uses the cosimplicial resolution J•X of a space X, to define the functors JnX=TotnJ•X. When n=∞ this is known as the completion functor. w that when J is a module triple, then the Bousfield–Kan functors Jn are triples on the homotopy category of spaces. In particular, when E is the spectrum of an S-algebra (or a symmetric spectrum), then the E-completion functor is up to homotopy a triple.