Up-to-homotopy algebras with strict units. (Extended abstract version.)
arXiv:1907.08422
Abstract
We prove the existence of minimal models a la Sullivan for operads with nontrivial arity zero. So up-to-homotopy algebras with strict units are just operad algebras over these minimal models. As an application, we give another proof of the formality of the unitary n-little disks operad over the rationals.
This is the "extended abstract version" of my preprint with the same title, arXiv:1811.10460. It was prepared to appear, eventually, in a book gathering together conference's talks. It might be useful if you want to get the idea of the main result and techniques of the original manuscript, without going through its 39 pages. This new version contains a change on one hypothesis of the results