Homotopy theory for generalised algebraic operads and their algebras
Roald Koudenburg (University of Sheffield)
Monday 5th December, 2011 15:00-16:00 416
The homotopy theory for classical operads and algebras over them is well understood. In more detail: we know what homotopy algebras are, how they can be transferred along weak equivalences and when they can be rectified to strict algebra structures. To start with we will recall these notions and results, working throughout in the category of chain complexes over a field of characteristic zero. We will then introduce classical operads as symmetric monoidal functors, as introduced by E. Getzler. Using this approach we can easily generalise to structures in which operations have multiple outputs (properads) or removing the distinction between inputs and outputs (cyclic operads). Following this we will think about how to obtain model structures on categories of such generalised operads, as well as on the categories of their (lax) algebras.