Theorems · Theorem · category theory
CategoryTheory.IsPushout.toCommSq
∀ {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.IsPushout f g inl inr → CategoryTheory.CommSq f g inl inr- Cited by
- 35 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.IsPushoutstatement and proof · cited by 219
- CategoryTheory.CommSqstatement · cited by 158
Cited by39
Results whose statement or proof uses this declaration.
- CategoryTheory.IsPushout.of_isoproof · cited by 10
- CategoryTheory.IsPushout.coconeproof · cited by 10
- CategoryTheory.IsPushout.inl_isoPushout_invproof · cited by 10
- CategoryTheory.IsPushout.inr_isoPushout_invproof · cited by 7
- CategoryTheory.IsPushout.opproof · cited by 7
- CategoryTheory.Functor.map_isPushoutproof · cited by 6
- CategoryTheory.IsPushout.unopproof · cited by 4
- CategoryTheory.IsPushout.isColimitCokernelCoforkstatement and proof · cited by 3
- CategoryTheory.IsPushout.isColimit'statement · cited by 2
- CategoryTheory.IsPushout.isVanKampen_iffstatement and proof · cited by 2
- CategoryTheory.IsPushout.IsVanKampen.exists_cube_fillingproof · cited by 2
- CategoryTheory.is_coprod_iff_isPushoutproof · cited by 1