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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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