Theorems · Definition · category theory

CategoryTheory.Equivalence.sheafCongrPreregular

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        [inst_2 : CategoryTheory.Preregular C] →
          (A : Type u_3) →
            [inst_3 : CategoryTheory.Category.{v_3, u_3} A] →
              (e : C ≌ D) →
                CategoryTheory.Sheaf (CategoryTheory.regularTopology C) A ≌
                  CategoryTheory.Sheaf (CategoryTheory.regularTopology D) A

Equivalent preregular categories give equivalent regular toposes.

Defined in

Mathlib.CategoryTheory.Sites.Coherent.Equivalence

Cited by

11 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreregularCategoryTheory.Category