Theorems · Definition · category theory
CategoryTheory.Limits.HasPushout
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y Z : C} → (X ⟶ Y) → (X ⟶ Z) → PropTwo morphisms f : X ⟶ Y and g : X ⟶ Z have a pushout if the diagram span f g has a
colimit.
- Cited by
- 192 results in Mathlib
- Foundations
- Depth 17 from the axioms, rests on 87 definitions · 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.Limits.HasColimitproof · cited by 307
- CategoryTheory.Limits.spanproof · cited by 294
Cited by241
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.pushoutstatement and proof · cited by 284
- CategoryTheory.Limits.pushout.inrstatement and proof · cited by 193
- CategoryTheory.Limits.pushout.inlstatement and proof · cited by 192
- CategoryTheory.IsPushout.isoPushoutstatement and proof · cited by 57
- CategoryTheory.Limits.pushout.descstatement and proof · cited by 46
- CategoryTheory.Functor.PushoutObjObj.ofHasPushoutstatement and proof · cited by 34
- CategoryTheory.Limits.pushoutSymmetrystatement and proof · cited by 30
- CategoryTheory.SmallObject.functorObjstatement and proof · cited by 30
- CategoryTheory.Limits.pushout.hom_extstatement and proof · cited by 30
- CategoryTheory.Limits.pushout.conditionstatement and proof · cited by 23
- CategoryTheory.SmallObject.ιFunctorObjstatement and proof · cited by 22
- CategoryTheory.IsPushout.of_hasPushoutstatement and proof · cited by 20
Showing the 200 most cited of 241.