Algebraic operads up to homotopy

Abstract

This paper deals with the homotopy theory of differential graded operads.
We endow the Koszul dual category of curved conilpotent cooperads, where
the notion of quasi-isomorphism barely makes sense, with a model category
structure Quillen equivalent to that of operads. This allows us to describe the
homotopy properties of differential graded operads in a simpler and richer way,
using obstruction methods.