Theorems · Theorem · category theory

CategoryTheory.Functor.isContinuous_comp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (F₁ : CategoryTheory.Functor C D)
  (F₂ : CategoryTheory.Functor D E) (J : CategoryTheory.GrothendieckTopology C)
  (K : CategoryTheory.GrothendieckTopology D) (L : CategoryTheory.GrothendieckTopology E) [F₁.IsContinuous J K]
  [F₂.IsContinuous K L], (F₁.comp F₂).IsContinuous J L

Defined in

Mathlib.CategoryTheory.Sites.Continuous

Cited by

11 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsContinuousCategoryTheory.Functor.IsContinuous