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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.

Defined in
Mathlib.CategoryTheory.Sites.Hypercover.One
Cited by
13 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.lift · cited by 4IsSheafIff.liftCategoryTheory.GrothendieckTopology.OneHypercover.isLimitMultifork · cited by 4OneHypercover.isLimitMult…CategoryTheory.PreOneHypercover.isLimitMapMultiforkEquiv · cited by 1PreOneHypercover.isLimitM…CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac' · cited by 1IsSheafIff.fac'CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc · cited by 1IsSheafIff.fac'_assocCategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.hom_ext · cited by 1IsSheafIff.hom_extCategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.isLimit · cited by 1IsSheafIff.isLimitCategoryTheory.PreZeroHypercover.isLimitSigmaOfIsColimitEquiv · cited by 1PreZeroHypercover.isLimit…CategoryTheory.PreZeroHypercover.isLimit_toPreOneHypercover_type_iff · cited by 1PreZeroHypercover.isLimit…CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff · cited by 1OneHypercoverDenseData.is…CategoryTheory.GrothendieckTopology.OneHypercoverFamily.isSheaf_iff · cited by 1OneHypercoverFamily.isShe…CategoryTheory.Presheaf.isSheaf_iff_of_isGeneratedByOneHypercovers · cited by 1Presheaf.isSheaf_iff_of_i…CategoryTheory.Presieve.isSheafFor_sigmaDesc_iff · cited by 1Presieve.isSheafFor_sigma…CategoryTheory.PreOneHypercover.isLimitEquivOfIso · cited by 0PreOneHypercover.isLimitE…CategoryTheory.PreOneHypercover.isLimitMultiforkEquivIsLimitFork · cited by 0PreOneHypercover.isLimitM…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.PreZeroHypercover.f · cited by 542PreZeroHypercover.fCategoryTheory.PreOneHypercover.toPreZeroHypercover · cited by 232PreOneHypercover.toPreZer…CategoryTheory.PreOneHypercover · cited by 180CategoryTheory.PreOneHype…CategoryTheory.Limits.MulticospanShape.L · cited by 135MulticospanShape.LCategoryTheory.Limits.Multifork · cited by 69Limits.MultiforkCategoryTheory.PreOneHypercover.multicospanShape · cited by 36PreOneHypercover.multicos…CategoryTheory.PreOneHypercover.multicospanIndex · cited by 27PreOneHypercover.multicos…CategoryTheory.Limits.Multifork.ofι · cited by 21Multifork.ofιPreOneHypercover.multiforkCITED BYCITES

Cites14

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Cited by25

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