under construction
For the (∞,1)-topos of E-∞ geometry, let
be the (∞,1)-category of (∞,1)-sheaves on the site of smooth manifolds with values in .
An object in this combines the properties of a smooth ∞-groupoid and an object in E-∞ geometry, hence might be called a “smooth -groupoid”.
It is useful to regard this as a cohesive (∞,1)-topos over
As such this appears for instance in the discussion at
Write
for the sheaf which sends each ring to its ∞-group of units
This is the canonical group object in . The mapping stacks into it are the Picard ∞-stacks.
(…)
For E-∞ rings over the complex numbers, hence E-∞ algebras over , the multiplicative group
naturally carries both the structure of an object in smooth ∞-groupoids and in E-∞ geometry, which may be combined to the structure of a smooth -groupoid.
For and let be given by
where on the right we have the ∞-groupoid underlying the abelian ∞-group which is the tensor product of the ∞-group of units of with the abelian group of non-vanishing complex-valued smooth functions on .
Last revised on May 21, 2014 at 12:50:22. See the history of this page for a list of all contributions to it.