Theorems · Theorem · category theory

CategoryTheory.Functor.isContinuous_of_coverPreserving

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {J : CategoryTheory.GrothendieckTopology C}
  {K : CategoryTheory.GrothendieckTopology D},
  CategoryTheory.CompatiblePreserving K F → CategoryTheory.CoverPreserving J K F → F.IsContinuous J K

If F is cover-preserving and compatible-preserving, then F is a continuous functor.

Defined in

Mathlib.CategoryTheory.Sites.CoverPreserving

Cited by

4 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category