Theorems · Theorem · category theory
CategoryTheory.Precoverage.toGrothendieck_le_iff_le_toPrecoverage
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_3, u_2} C] {K : CategoryTheory.Precoverage C}
{J : CategoryTheory.GrothendieckTopology C}, K.toGrothendieck ≤ J ↔ K ≤ J.toPrecoveragetoGrothendieck and toPrecoverage form a Galois connection.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Sieveproof · cited by 552
- CategoryTheory.Presieveproof · cited by 449
- CategoryTheory.Sieve.arrowsproof · cited by 446
- CategoryTheory.Precoveragestatement and proof · cited by 204
- CategoryTheory.Precoverage.coveringsproof · cited by 194
- CategoryTheory.Sieve.pullbackproof · cited by 126
- CategoryTheory.Sieve.generateproof · cited by 117
- CategoryTheory.Precoverage.toGrothendieckstatement and proof · cited by 41
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.galoisConnection_toGrothendieck_toPrecoverageproof · cited by 6
- CategoryTheory.over_toGrothendieck_eq_toGrothendieck_comap_forgetproof · cited by 3
- CategoryTheory.Precoverage.Generates.toGrothendieck_eqproof · cited by 1
- CategoryTheory.Coverage.generates_toGrothendieckproof · cited by 1