Theorems · Inductive type · category theory

CategoryTheory.Functor.IsContinuous

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

A functor F is continuous if the precomposition with F.op sends sheaves of Type (max u₁ v₁ u₂ v₂) to sheaves. This implies that this holds for an arbitrary universe (see Functor.op_comp_isSheaf_of_types).

Defined in

Mathlib.CategoryTheory.Sites.Continuous

Cited by

100 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 4 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category