operadic (∞,1)-Grothendieck construction
Algebras and modules
Model category presentations
Geometry on formal duals of algebras
The operadic (∞,1)-Grothendieck construction is the generalization of the (∞,1)-Grothendieck construction from (∞,1)-categories to (∞,1)-operads.
Notice that where in the categorical context we had pseudofunctors
and then in the (∞,1)-category theoretic context (∞,1)-functors
as input if the Grothendieck construction, in the (∞,1)-operadic context such morphisms
have the interpretation of ∞-algebra over an (∞,1)-operad.
Equivalence between -Algebras and fibrations
For an (∞,1)-operad, there is an equivalence of (∞,1)-categories between ∞-algebras over in (∞,1)Cat and opCartesian fibrations into .
This is the central theorem in (Heuts).
A construction modeled on dendroidal sets is discussed in
In section 2.1.3 of
the statement of the above equivalence is essentially taken as a definition.
Created on February 15, 2012 02:31:44
by Urs Schreiber