Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.hom_ext_yoneda

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C)
  [inst_1 : J.Subcanonical] {P Q : CategoryTheory.Sheaf J (Type v)} {f g : P ⟶ Q},
  (∀ (X : C) (p : J.yoneda.obj X ⟶ P),
      CategoryTheory.CategoryStruct.comp p f = CategoryTheory.CategoryStruct.comp p g) →
    f = g

Two morphisms of sheaves of types P ⟶ Q coincide if the precompositions with morphisms yoneda.obj X ⟶ P agree.

Defined in

Mathlib.CategoryTheory.Sites.Subcanonical

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GrothendieckTopology.Subcanonical