## Mapping spaces and internal algebra classifiers

### Michael Batanin – 15 March 2017

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 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 more conceptual perspective using the theory of internal algebra classifiers.

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