Summary: All algebraic objects in this note will be considered over a fixed field $k$ of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over $k$. For standard terminology concerning operads, algebras over operads, etc., see either the original paper by J. P. May [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [J.-L. Loday, “La renaissance des opérads”, Sémin. Bourbaki 1994/95, Exp. No. 792, Asterisque 237, 47-74 (1996; Zbl 0866.18007)].The aim of this note is mainly to advocate our approach to homotopy algebras based on the minimal model of an operad. Our intention is to expand it to a paper on homotopy properties of the category of homotopy algebras; some possible results in this direction are indicated in Section 3.

EUDML-ID : urn:eudml:doc:221254
Mots clés:

@article{701658,
     title = {Homotopy algebras via resolutions of operads},
     booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2000},
     pages = {157-164},
     mrnumber = {MR1758091},
     zbl = {0962.18007},
     url = {http://dml.mathdoc.fr/item/701658}
}

Markl, Martin. Homotopy algebras via resolutions of operads, dans Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books,  (2000), pp. 157-164. http://gdmltest.u-ga.fr/item/701658/