Theorems · Theorem · category theory

CategoryTheory.Limits.PushoutCocone.condition_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z}
  (t : CategoryTheory.Limits.PushoutCocone f g),
  t.ι.app CategoryTheory.Limits.WalkingSpan.zero = CategoryTheory.CategoryStruct.comp f t.inl

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
Cited by: 4 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites20

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.Functor.mapproof · cited by 8,698
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.Limits.Cocone.ptstatement and proof · cited by 1,354
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Functor.conststatement and proof · cited by 1,264
CategoryTheory.Limits.Cocone.ιstatement and proof · cited by 605

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.IsPushout.isVanKampen_iffproof · cited by 2
CategoryTheory.Limits.Types.eq_or_eq_of_isPushoutproof · cited by 1
CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_noneproof · cited by 0
CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_noneproof · cited by 0