symmetric monoidal (∞,1)-category of spectra
Let be an (∞,1)-operad. A coCartesian fibration of (∞,1)-operads is
a coCartesian fibration of the underlying quasi-categories;
such that the composite
exhibits as an (∞,1)-operad.
In this case we say that the underlying (∞,1)-category
is equipped by with the structure of an -monoidal (∞,1)-category (see remark below).
This is (Lurie, def. 2.1.2.13).
For a coCartesian fibration of -operads by def. , the underlying map
is a coCartesian fibration of (∞,1)-categories. Therefore by the (∞,1)-Grothendieck construction it is classified by an (∞,1)-functor
This inherits monoidal structure (with respect to the cartesian monoidal (∞,1)-category structure on (∞,1)Cat) and hence exhibits an -algebra in (∞,1)Cat. This way coCartesian fibrations of -operads over some are equivalently -algebras in (∞,1)Cat. Therefore their identification with -monoidal (∞,1)-categories.
(Lurie, remark 2.1.2.17, 2.4.2.6)
coCartesian fibration of (∞,1)-operads
Last revised on February 12, 2013 at 05:40:48. See the history of this page for a list of all contributions to it.