Cohomology and homotopy
In higher category theory
For a ringed topos the ring object is called the structure sheaf.
More generally, for a geometry (for structured (∞,1)-toposes), a structured (∞,1)-topos
is an (∞,1)-topos equipped with a -valued structure sheaf presented by the finite-limits-preserving and cover-preserving (∞,1)-functor .
In particular for an