Theorems · Definition · category theory
CategoryTheory.GrothendieckTopology.toPrecoverage
{C : Type u_2} →
[inst : CategoryTheory.Category.{u_3, u_2} C] → CategoryTheory.GrothendieckTopology C → CategoryTheory.Precoverage CThe induced coverage by a Grothendieck topology as a precoverage.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 32 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.
Cites7
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
- Set.ofPredproof · cited by 6,101
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Presieveproof · cited by 449
- CategoryTheory.Precoveragestatement · cited by 204
- CategoryTheory.Sieve.generateproof · cited by 117
Cited by16
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.restrictedTopologyproof · cited by 14
- CategoryTheory.Precoverage.galoisConnection_toGrothendieck_toPrecoveragestatement · cited by 6
- CategoryTheory.Precoverage.toGrothendieck_le_iff_le_toPrecoveragestatement and proof · cited by 4
- CategoryTheory.Functor.coverPreserving_restrictedTopologyproof · cited by 3
- CategoryTheory.GrothendieckTopology.mem_toPrecoverage_iffstatement · cited by 3
- CategoryTheory.Precoverage.Generates.le_toPrecoveragestatement · cited by 3
- CategoryTheory.Precoverage.toGrothendieck_comap_le_restrictedTopologyproof · cited by 2
- CategoryTheory.GrothendieckTopology.OneHypercover.toZeroHypercoverstatement · cited by 1
- CategoryTheory.Precoverage.le_toPrecoverage_toGrothendieckstatement · cited by 1
- CategoryTheory.GrothendieckTopology.OneHypercover.toZeroHypercover_toPreZeroHypercoverstatement · cited by 0
- CategoryTheory.GrothendieckTopology.arrows_mem_toPrecoverage_iffstatement · cited by 0
- CategoryTheory.Precoverage.Generates.casesOnstatement and proof · cited by 0