Theorems · Inductive type · category theory
CategoryTheory.Precoverage.Generates
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
CategoryTheory.Precoverage C → CategoryTheory.GrothendieckTopology C → PropA precoverage K generates the topology J if a presheaf on C is a sheaf
for K if and only if it is a sheaf for J.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- CategoryTheory.Precoveragestatement · cited by 204
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.Generates.le_toPrecoveragestatement and proof · cited by 3
- CategoryTheory.Coverage.generates_toGrothendieckstatement · cited by 1
- CategoryTheory.Precoverage.Generates.isSheaf_of_forallstatement and proof · cited by 1
- CategoryTheory.Precoverage.Generates.isSheaf_type_iffstatement and proof · cited by 1
- CategoryTheory.Precoverage.Generates.toGrothendieck_eqstatement and proof · cited by 1
- CategoryTheory.Coverage.generates_iffstatement and proof · cited by 0
- CategoryTheory.Precoverage.Generates.casesOnstatement and proof · cited by 0
- CategoryTheory.Precoverage.Generates.generate_memstatement and proof · cited by 0
- CategoryTheory.Precoverage.Generates.isSheaf_iffstatement and proof · cited by 0
- CategoryTheory.Precoverage.Generates.isSheaf_of_forall_maxstatement and proof · cited by 0
- CategoryTheory.Precoverage.Generates.recOnstatement and proof · cited by 0