Theorems · Theorem · category theory
CategoryTheory.IsPushout.of_horiz_isIso_epi
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {Z X Y P : C} {f : Z ⟶ X} {g : Z ⟶ Y} {inl : X ⟶ P}
{inr : Y ⟶ P} [CategoryTheory.Epi f] [CategoryTheory.IsIso inr],
CategoryTheory.CommSq f g inl inr → CategoryTheory.IsPushout f g inl inr- Cited by
- 2 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Limits.Cocone.ptproof · cited by 1,354
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.invproof · cited by 467
- CategoryTheory.cancel_epiproof · cited by 380
- CategoryTheory.IsPushoutstatement · cited by 219
- CategoryTheory.CommSqstatement and proof · cited by 158
- CategoryTheory.CommSq.wproof · cited by 122
- CategoryTheory.Limits.PushoutCoconeproof · cited by 66
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.IsPushout.of_horiz_isIsoproof · cited by 4
- CategoryTheory.IsPushout.of_vert_isIso_epiproof · cited by 1