homotopy coinvariants functor
Given a monoidal category and a comonoid in with coaugmentation , one can define the following pair of adjoint functors:
where denotes the cotensor product bifunctor and is a right -coaction. is called the (co)free or trivial comodule functor and the functor of coinvariants.
If is in fact a monoidal model category, then we can ask whether this pair of functors is a Quillen pair. If so then the the homotopy coinvariants functor is the total right derived functor
Given a -comodule , any representative of is called a model of the homotopy coinvariants of .
- K. Hess, Homotopic Hopf-Galois extensions: foundations and examples, arxiv/0902.3393
Revised on November 14, 2013 23:07:45
by Urs Schreiber