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)- 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.
Cites23
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
- CategoryTheory.Functor.constproof · cited by 1,264
- CategoryTheory.Limits.Cone.πproof · cited by 500
- CategoryTheory.Limits.WalkingMulticospanstatement and proof · cited by 199
- CategoryTheory.Limits.MulticospanIndex.multicospanstatement and proof · cited by 167
- CategoryTheory.Limits.MulticospanShapestatement and proof · cited by 160
- CategoryTheory.Limits.MulticospanShape.Rstatement and proof · cited by 124
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Multiequalizer.conditionproof · cited by 3
- CategoryTheory.Limits.Wedge.conditionproof · cited by 3
- CategoryTheory.Limits.Multifork.isoOfιstatement · cited by 2
- CategoryTheory.Limits.Multifork.pi_conditionproof · cited by 2
- CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_mapproof · cited by 2
- CategoryTheory.PreOneHypercover.Homotopy.mapMultiforkOfIsLimit_eqproof · cited by 0
- CategoryTheory.Limits.Multifork.isoOfι_hom_homstatement · cited by 0
- CategoryTheory.Limits.Multifork.isoOfι_inv_homstatement · cited by 0
- CategoryTheory.PreOneHypercover.Hom.mapMultiforkOfIsLimit_idstatement and proof · cited by 0
- CategoryTheory.Limits.Multifork.condition_assocproof · cited by 0
- CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.facproof · cited by 0