mathlib documentation

algebraic_geometry.stalks

Stalks for presheaved spaces #

This file lifts constructions of stalks and pushforwards of stalks to work with the category of presheafed spaces. Additionally, we prove that restriction of presheafed spaces does not change the stalks.

The stalk at x of a PresheafedSpace.

Equations

For an open embedding f : U ⟶ X and a point x : U, we get an isomorphism between the stalk of X at f x and the stalk of the restriction of X along f at t x.

Equations

If α = β and x = x', we would like to say that stalk_map α x = stalk_map β x'. Unfortunately, this equality is not well-formed, as their types are not definitionally the same. To get a proper congruence lemma, we therefore have to introduce these eq_to_hom arrows on either side of the equality.