symmetric monoidal (∞,1)-category of spectra
The notion of module over an associative algebra has a generalization to a notion of modules over an algebra that is an algebra over an operad.
Note that sometimes an algebra over an operad is called a module over the operad, so here we have a module over a module. (Whether algebras/modules over operads are more like algebras or more like modules depends on your point of view, so both terms are used.)
Let be a closed symmetric monoidal category, an operad in and a -algebra over an operad.
A module over consists of
an object ;
for all a morphism
in (the action morphims)
such that this data satisfies
unitality (…)
associativity (…)
equivariance (…)
Under suitable conditions there is a model structure on modules over an algebra over an operad.
-modules, etc.
(…)
A review of modules over algebras over operads is at the beginning of
Last revised on September 1, 2012 at 19:50:17. See the history of this page for a list of all contributions to it.