higher geometry / derived geometry
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geometric little (∞,1)-toposes
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A deformation context is an (∞,1)-category such that
it is a presentable (∞,1)-category;
it contains a terminal object
together with a set of objects in the stabilization of .
This is (Lurie, def. 1.1.3) together with the assumption of a terminal object stated (and later implicialy used) on p.9.
Definition is meant to be read as follows:
First, we think of as an opposite (∞,1)-category of pointed spaces in some higher geometry. The point is the initial object in which is the terminal object in .
Then we think of the formal duals of the objects as a set of generating infinitesimally thickened points.
The following construction generates the “jets” induced by the generating infinitesimally thickened points.
Given a deformation context , we say
a morphism in is an elementary morphism if it is the homotopy fiber to a map into for some and some ;
a morphism is a small morphism if it is the composite of finitely many elementary morphisms.
We write
for the full sub-(∞,1)-category on those objects for which the essentially unique map is small.
Created on February 7, 2013 at 17:40:12. See the history of this page for a list of all contributions to it.