Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.Limits.Multifork.condition

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Limits.MulticospanShape}
  {I : CategoryTheory.Limits.MulticospanIndex J C} (K : CategoryTheory.Limits.Multifork I) (b : J.R),
  CategoryTheory.CategoryStruct.comp (K.ι (J.fst b)) (I.fst b) =
    CategoryTheory.CategoryStruct.comp (K.ι (J.snd b)) (I.snd b)
Defined in
Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
Cited by
10 results in Mathlib
Foundations
Depth 25 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.

CategoryTheory.Limits.Multiequalizer.condition · cited by 3Multiequalizer.conditionCategoryTheory.Limits.Wedge.condition · cited by 3Wedge.conditionCategoryTheory.Limits.Multifork.isoOfι · cited by 2Multifork.isoOfιCategoryTheory.Limits.Multifork.pi_condition · cited by 2Multifork.pi_conditionCategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map · cited by 2RanIsSheafOfIsCocontinuou…CategoryTheory.PreOneHypercover.Homotopy.mapMultiforkOfIsLimit_eq · cited by 0Homotopy.mapMultiforkOfIs…CategoryTheory.Limits.Multifork.isoOfι_hom_hom · cited by 0Multifork.isoOfι_hom_homCategoryTheory.Limits.Multifork.isoOfι_inv_hom · cited by 0Multifork.isoOfι_inv_homCategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_id · cited by 0Hom.mapMultiforkOfIsLimit…CategoryTheory.Limits.Multifork.condition_assoc · cited by 0Multifork.condition_assocCategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac · cited by 0IsSheafIff.facCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Limits.Cone.pt · cited by 1298Cone.ptCategoryTheory.Functor.const · cited by 1264Functor.constCategoryTheory.Limits.Cone.π · cited by 500Cone.πCategoryTheory.Limits.WalkingMulticospan · cited by 199Limits.WalkingMulticospanCategoryTheory.Limits.MulticospanIndex.multicospan · cited by 167MulticospanIndex.multicos…CategoryTheory.Limits.MulticospanShape · cited by 160Limits.MulticospanShapeCategoryTheory.Limits.MulticospanShape.R · cited by 124MulticospanShape.RCategoryTheory.Limits.MulticospanIndex.left · cited by 119MulticospanIndex.leftCategoryTheory.Limits.MulticospanIndex · cited by 101Limits.MulticospanIndexCategoryTheory.Limits.MulticospanIndex.right · cited by 77MulticospanIndex.rightMultifork.conditionCITED BYCITES

Cites23

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.