Theorems · Definition · category theory

CategoryTheory.Functor.inducedTopology

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        CategoryTheory.Functor C D → CategoryTheory.GrothendieckTopology D → CategoryTheory.GrothendieckTopology C

The induced topology by a topology on D along a functor F : C ⥤ D is the finest topology on C making F continuous. [SGA4, III, 3.1][sga-4-tome-1]

Defined in

Mathlib.CategoryTheory.Sites.InducedTopology

Cited by

19 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category