Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective.transport

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (K : CategoryTheory.GrothendieckTopology D)
  (G : CategoryTheory.Functor D C) {A : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} A] [G.IsCoverDense J]
  [G.Full] [inst_5 : G.IsContinuous K J] [(G.sheafPushforwardContinuous A K J).EssSurj] [G.IsCocontinuous K J]
  {FA : A → A → Type u_1} {CA : A → Type u_2} [inst_8 : (X Y : A) → FunLike (FA X Y) (CA X) (CA Y)]
  [inst_9 : CategoryTheory.ConcreteCategory A FA] [K.WEqualsLocallyBijective A],
  CategoryTheory.CoverPreserving K J G → J.WEqualsLocallyBijective A

Defined in

Mathlib.CategoryTheory.Sites.Equivalence

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsCoverDenseCategoryTheory.Functor.FullCategoryTheory.Functor.IsContinuousCategoryTheory.Functor.EssSurjCategoryTheory.Functor.IsCocontinuousFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective