This is a report on our work in progress with Florian de Leger. A result of Dwyer-Hess and Tourchin asserts that there is a weak equivalence of double loop space of over homotopy mapping spaces from the associativity operad Ass to any nonsymmetric operad O with O(0) = O(1) = 1 and the homotopy space of weak Ass-bimodule maps from Ass to O. We explain this result from a more conceptual perspective using the theory of internal algebra classifiers.