Theorems · Definition · category theory
CategoryTheory.PreOneHypercover.multifork
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{A : Type u_1} →
[inst_1 : CategoryTheory.Category.{v_1, u_1} A] →
{S : C} →
(E : CategoryTheory.PreOneHypercover S) →
(F : CategoryTheory.Functor Cᵒᵖ A) → CategoryTheory.Limits.Multifork (E.multicospanIndex F)The multifork attached to a presheaf F : Cᵒᵖ ⥤ A, S : C and E : PreOneHypercover S.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.PreZeroHypercover.fproof · cited by 542
- CategoryTheory.PreOneHypercover.toPreZeroHypercoverproof · cited by 232
- CategoryTheory.PreOneHypercoverstatement and proof · cited by 180
- CategoryTheory.Limits.MulticospanShape.Lproof · cited by 135
- CategoryTheory.Limits.Multiforkstatement · cited by 69
- CategoryTheory.PreOneHypercover.multicospanShapestatement and proof · cited by 36
Cited by25
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.liftstatement and proof · cited by 4
- CategoryTheory.GrothendieckTopology.OneHypercover.isLimitMultiforkstatement and proof · cited by 4
- CategoryTheory.PreOneHypercover.isLimitMapMultiforkEquivstatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'statement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assocstatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.hom_extstatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.isLimitstatement and proof · cited by 1
- CategoryTheory.PreZeroHypercover.isLimitSigmaOfIsColimitEquivstatement · cited by 1
- CategoryTheory.PreZeroHypercover.isLimit_toPreOneHypercover_type_iffstatement and proof · cited by 1
- CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iffstatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.OneHypercoverFamily.isSheaf_iffstatement and proof · cited by 1
- CategoryTheory.Presheaf.isSheaf_iff_of_isGeneratedByOneHypercoversstatement · cited by 1