Manifolds and cobordisms
An atlas is a compatible collection of coordinate charts.
In full generality, for a pregeometry and an object in the (∞,1)-sheaf (∞,1)-topos, an atlas for is a collection of suitable morphisms (open maps) with , such that the morphism out of the coproduct
\coprod_i U_i \to X
is an effective epimorphism.
For geometric stacks
Revised on August 18, 2013 14:24:42
by Urs Schreiber