Theorems · Definition · algebraic geometry

CategoryTheory.MorphismProperty.pretopology

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasPullbacks C] →
      (P : CategoryTheory.MorphismProperty C) →
        [P.IsMultiplicative] → [P.IsStableUnderBaseChange] → CategoryTheory.Pretopology C

If P is a multiplicative morphism property which is stable under base change on a category C with pullbacks, then P induces a pretopology, where coverings are given by presieves whose elements satisfy P.

Defined in

Mathlib.CategoryTheory.Sites.MorphismProperty

Cited by

8 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderBaseChange