Theorems · Definition · algebraic geometry

CategoryTheory.MorphismProperty.grothendieckTopology

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

If P is stable under base change, it induces a Grothendieck topology: the one associated to coverage P.

Defined in: Mathlib.CategoryTheory.Sites.MorphismProperty
Cited by: 1 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MorphismProperty.IsStableUnderBaseChange CategoryTheory.MorphismProperty.HasPullbacks

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.GrothendieckTopologystatement · cited by 1,415
CategoryTheory.MorphismProperty.IsStableUnderBaseChangestatement and proof · cited by 131
CategoryTheory.Coverage.toGrothendieckproof · cited by 15
CategoryTheory.MorphismProperty.HasPullbacksstatement and proof · cited by 4
CategoryTheory.MorphismProperty.coverageproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.grothendieckTopology_eq_toGrothendieck_pretopologystatement · cited by 0