Theorems · Theorem · category theory

CategoryTheory.Limits.Trident.app_zero

∀ {J : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : J → (X ⟶ Y)}
  (s : CategoryTheory.Limits.Trident f) (j : J),
  CategoryTheory.CategoryStruct.comp (s.π.app CategoryTheory.Limits.WalkingParallelFamily.zero) (f j) =
    s.π.app CategoryTheory.Limits.WalkingParallelFamily.one

Defined in: Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers
Cited by: 3 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Functor.conststatement · cited by 1,264
CategoryTheory.Limits.Cone.πstatement and proof · cited by 500
CategoryTheory.Limits.WalkingParallelFamilystatement · cited by 61
CategoryTheory.Limits.parallelFamilystatement and proof · cited by 58
CategoryTheory.Limits.Cone.wproof · cited by 40

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Trident.conditionproof · cited by 2
CategoryTheory.Limits.Trident.equalizer_extproof · cited by 1
CategoryTheory.Limits.Trident.app_zero_assocproof · cited by 0