locally ringed space
Cohomology and homotopy
In higher category theory
A locally ringed space is a ringed space such that the stalks of the structure sheaf are local rings.
A morphism of locally ringed space is a morphism of ringed spaces , where , such that the comorphism is a morphism of local rings (that is, a map of rings which respects the maximal ideal).
Section 19.2 in