Commit 2020-09-11 17:48 045619ea
View on Github →feat(topology/sheaves): sheafification (#3937)
Sheafification of Type
valued presheaves
We construct the sheafification of a Type
valued presheaf,
as the subsheaf of dependent functions into the stalks
consisting of functions which are locally germs.
We show that the stalks of the sheafification are isomorphic to the original stalks,
via stalk_to_fiber
which evaluates a germ of a dependent function at a point.
We construct a morphism to_sheafify
from a presheaf to (the underlying presheaf of)
its sheafification, given by sending a section to its collection of germs.
Future work
Show that the map induced on stalks by to_sheafify
is the inverse of stalk_to_fiber
.
Show sheafification is a functor from presheaves to sheaves,
and that it is the left adjoint of the forgetful functor.