Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_injective

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} (Φ : J.Point)
  {A : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} A]
  [inst_2 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A] {FC : A → A → Type u_1} {CC : A → Type w'}
  [inst_3 : (X Y : A) → FunLike (FC X Y) (CC X) (CC Y)] [inst_4 : CategoryTheory.ConcreteCategory A FC]
  {P Q : CategoryTheory.Functor Cᵒᵖ A}
  [CategoryTheory.Limits.PreservesFilteredColimitsOfSize.{w, w, v', w', u', w' + 1} (CategoryTheory.forget A)]
  [CategoryTheory.LocallySmall.{w, v, u} C] (f : P ⟶ Q) [CategoryTheory.Presheaf.IsLocallyInjective J f],
  Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (Φ.presheafFiber.map f))

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

1 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSizeFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.Limits.PreservesFilteredColimitsOfSizeCategoryTheory.LocallySmallCategoryTheory.Presheaf.IsLocallyInjective