Theorems · Definition · category theory

TopCat.Presheaf.germ

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasColimits C] →
      {X : TopCat} →
        (F : TopCat.Presheaf C X) →
          (U : TopologicalSpace.Opens ↑X) → (x : ↑X) → x ∈ U → (F.obj (Opposite.op U) ⟶ F.stalk x)

The germ of a section of a presheaf over an open at a point of that open.

Defined in

Mathlib.Topology.Sheaves.Stalks

Cited by

208 results in Mathlib

Foundations

Depth 38 from the axioms, rests on 253 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimits