6 research outputs found
A model structure for coloured operads in symmetric spectra
We describe a model structure for coloured operads with values in the
category of symmetric spectra (with the positive model structure), in which
fibrations and weak equivalences are defined at the level of the underlying
collections. This allows us to treat R-module spectra (where R is a cofibrant
ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as
its first term. Using this model structure, we give suficient conditions for
homotopical localizations in the category of symmetric spectra to preserve
module structures.Comment: 16 page
Smash products for secondary homotopy groups
We construct a smash product operation on secondary homotopy groups yielding
the structure of a lax symmetric monoidal functor. Applications on cup-one
products, Toda brackets and Whitehead products are considered. In particular we
prove a formula for the crossed effect of the cup-one product operation on
unstable homotopy groups of spheres which was claimed by
Barratt-Jones-Mahowald.Comment: We give a clearer description of the tensor product of symmetric
sequences of quadratic pair module