## Mapping spaces and internal algebra classifiers

### Florian De Leger – 3 May 2017

This is a report on our work in progress with Michael Batanin. 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, continuing the talk of Michael Batanin on Wednesday 15 March 2017.

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