Theorems · Definition · category theory

CategoryTheory.Precoverage.toPretopology

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasPullbacks C] →
      (J : CategoryTheory.Precoverage C) →
        [J.HasIsos] → [J.IsStableUnderBaseChange] → [J.IsStableUnderComposition] → CategoryTheory.Pretopology C

If J is a precoverage that has isomorphisms and is stable under composition and base change, it defines a pretopology.

Defined in

Mathlib.CategoryTheory.Sites.Pretopology

Cited by

6 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.Precoverage.HasIsosCategoryTheory.Precoverage.IsStableUnderBaseChangeCategoryTheory.Precoverage.IsStableUnderComposition