Theorems · Theorem · category theory

CategoryTheory.Limits.FormalCoproduct.isPullback

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : CategoryTheory.Limits.FormalCoproduct C} (f : X ⟶ Z)
  (g : Y ⟶ Z)
  (pb :
    (i : Function.Pullback f.f g.f) →
      CategoryTheory.Limits.PullbackCone (CategoryTheory.CategoryStruct.comp (f.φ (↑i).1) (CategoryTheory.eqToHom ⋯))
        (g.φ (↑i).2))
  (hpb : (i : Function.Pullback f.f g.f) → CategoryTheory.Limits.IsLimit (pb i)),
  CategoryTheory.IsPullback (CategoryTheory.Limits.FormalCoproduct.pullbackCone f g pb).fst
    (CategoryTheory.Limits.FormalCoproduct.pullbackCone f g pb).snd f g

Defined in: Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
CategoryTheory.eqToHomstatement and proof · cited by 860
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
CategoryTheory.Limits.WalkingCospanstatement · cited by 496
CategoryTheory.Limits.cospanstatement · cited by 467
CategoryTheory.IsPullbackstatement · cited by 320
CategoryTheory.Limits.PullbackConestatement and proof · cited by 136
CategoryTheory.Limits.FormalCoproductstatement and proof · cited by 122

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