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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 {\it J. P. May} [``The geometry of iterated loop spaces'', Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [{\it J.-L. Loday}, ``La renaissance des op\'erads'', S\'emin. Bourbaki 1994/95, Exp. No. 792, Asterisque 237, 47-74 (1996; Zbl 0866.18007)].\par 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. (English) |
