Homological algebra of homotopy algebras
Abstract
Description
We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed operad, on the category of modules over a fixed operad algebra. In Sections 2 - 6 we define the necessary structures and provide some standard comparison results. In Section 7 we define cotangent complex. In Section 8 we define a canonical structure of homotopy Lie algebra on the tangent complex.
AMS-LaTeX v1.2 (Compatibility mode), 39 pages
AMS-LaTeX v1.2 (Compatibility mode), 39 pages