Commit 2020-09-11 17:48 045619eaView on Github →
feat(topology/sheaves): sheafification (#3937)
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,
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.
Show that the map induced on stalks by
to_sheafify is the inverse of
Show sheafification is a functor from presheaves to sheaves,
and that it is the left adjoint of the forgetful functor.