Algebras and modules
Model category presentations
Geometry on formal duals of algebras
An -algebra is an algebra over an operad for an E-∞ operad.
In chain complexes
-algebras in chain complexes are equivalent to those in abelian simplicial group.
For details on this statement see monoidal Dold-Kan correspondence and operadic Dold-Kan correspondence.
In topological spaces
In simplicial sets
This is in BergerMoerdijk I, BergerMoerdijk II.
An -algebra in spectra is an E-∞ ring.
See symmetric monoidal (∞,n)-category.
- Martin Markl, Steve Shnider, Jim Stasheff, Operads in algebra, topology and physics, Math. Surveys and Monographs 96, Amer. Math. Soc. 2002.
In the context of (infinity,1)-operads -algebras are discussed in
A systematic study of model category structures on operads and their algebras is in
The induced model structures and their properties on algebras over operads are discussed in
Revised on October 18, 2014 12:41:37
by Urs Schreiber