Theorems · Definition · category theory
CategoryTheory.Sieve.giGenerate
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X : C} → GaloisInsertion CategoryTheory.Sieve.generate CategoryTheory.Sieve.arrowsShow that there is a Galois insertion (generate, underlying presieve).
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 28 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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Sievestatement · cited by 552
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Sieve.arrowsstatement and proof · cited by 446
- CategoryTheory.Sieve.generatestatement and proof · cited by 117
- GaloisInsertionstatement · cited by 35
- CategoryTheory.Sieve.generate_le_iffproof · cited by 16
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Sieve.le_generateproof · cited by 20
- CategoryTheory.Sieve.generate_sieveproof · cited by 19
- CategoryTheory.Sieve.generate_monoproof · cited by 3
- AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iffproof · cited by 1
- CategoryTheory.Presieve.isSheaf_pretopologyproof · cited by 1
- CategoryTheory.Sieve.generate_eq_bot_iffproof · cited by 0
- CategoryTheory.Sieve.arrows_monoproof · cited by 0