Theorems · Theorem · category theory
CategoryTheory.GrothendieckTopology.eq_top_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C),
J = ⊤ ↔ ∀ (X : C), ⊥ ∈ J X- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Top.topstatement and proof · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Sievestatement and proof · cited by 552
- bot_leproof · cited by 306
- eq_top_iffproof · cited by 236
- CategoryTheory.GrothendieckTopology.superset_coveringproof · cited by 37
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.eq_top_of_isEmptyproof · cited by 1
- AlgebraicGeometry.Scheme.ProEt.topology_eq_top_of_isEmptyproof · cited by 1