symmetric monoidal (∞,1)-category of spectra
equivalences in/of $(\infty,1)$-categories
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.
For $P$ an (∞,1)-operad, there is an equivalence of (∞,1)-categories between ∞-algebras over $P$ in (∞,1)Cat and opCartesian fibrations into $P$.
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 at 02:10:49. See the history of this page for a list of all contributions to it.