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Homotopy algebras via resolutions of operads. (English) Zbl 0962.18007
Slovák, Jan (ed.) et al., The proceedings of the 19th Winter School “Geometry and physics”, Srní, Czech Republic, January 9-15, 1999. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 63, 157-164 (2000).
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.
For the entire collection see [Zbl 0940.00040].

##### MSC:
 18D50 Operads (MSC2010) 55P48 Loop space machines and operads in algebraic topology 18G55 Nonabelian homotopical algebra (MSC2010) 55P35 Loop spaces
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