Theorems · Definition · category theory

CategoryTheory.Sheaf.locallyInjective

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      (A : Type u') →
        [inst_1 : CategoryTheory.Category.{v', u'} A] →
          {FA : A → A → Type u_1} →
            {CA : A → Type w} →
              [inst_2 : (X Y : A) → FunLike (FA X Y) (CA X) (CA Y)] →
                [CategoryTheory.ConcreteCategory A FA] → CategoryTheory.MorphismProperty (CategoryTheory.Sheaf J A)

The class of locally injective morphisms of sheaves, see Sheaf.IsLocallyInjective.

Defined in

Mathlib.CategoryTheory.Sites.EpiMono

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory