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,
stalkToFiber which evaluates a germ of a dependent function at a point.
We construct a morphism
toSheafify from a presheaf to (the underlying presheaf of)
its sheafification, given by sending a section to its collection of germs.
Future work #
Show sheafification is a functor from presheaves to sheaves, and that it is the left adjoint of the forgetful functor, following https://stacks.math.columbia.edu/tag/007X.
The natural morphism from the stalk of the sheafification to the original stalk.
sheafifyStalkIso we show this is an isomorphism.