Theorems · Inductive type · category theory
CategoryTheory.Presieve.ofArrows
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X : C} → {ι : Type u_1} → (Y : ι → C) → ((i : ι) → Y i ⟶ X) → CategoryTheory.Presieve XConstruct the presieve given by the family of arrows indexed by ι.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 150 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 8 definitions · 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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Presievestatement · cited by 449
Cited by174
Results whose statement or proof uses this declaration.
- CategoryTheory.PreZeroHypercover.presieve₀proof · cited by 70
- CategoryTheory.Presieve.ofArrows.casesOnstatement and proof · cited by 64
- CategoryTheory.Sieve.ofArrowsproof · cited by 55
- CategoryTheory.Presieve.map_ofArrowsstatement and proof · cited by 14
- CategoryTheory.Presieve.ofArrows_le_iffstatement and proof · cited by 10
- CategoryTheory.Presieve.ofArrows_pUnitstatement · cited by 10
- CategoryTheory.regularCoverageproof · cited by 9
- CategoryTheory.Presieve.exists_eq_ofArrowsstatement and proof · cited by 8
- CategoryTheory.Precoverage.mem_iff_exists_zeroHypercoverstatement and proof · cited by 8
- CategoryTheory.Equalizer.Presieve.Arrows.SecondObjstatement and proof · cited by 7
- CategoryTheory.Presieve.isSheafFor_arrows_iffstatement and proof · cited by 7
- CategoryTheory.extensiveCoverageproof · cited by 7