Theorems · Definition · category theory
CategoryTheory.Limits.HasPushoutsAlong
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y : C} → (X ⟶ Y) → PropHasPushoutsAlong f states that pushouts of all morphisms out of X
along f : X ⟶ Y exist.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.HasPushoutproof · cited by 192
Cited by14
Results whose statement or proof uses this declaration.
- CategoryTheory.Under.pushoutstatement and proof · cited by 21
- CategoryTheory.Under.mapPushoutAdjstatement and proof · cited by 4
- CategoryTheory.MorphismProperty.Under.pushoutCompForgetIsostatement and proof · cited by 4
- CategoryTheory.Limits.hasPushouts_symmetry_of_hasPushoutsAlongstatement and proof · cited by 1
- CategoryTheory.Under.mapPushoutAdj_unit_appstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.underPushoutMapstatement and proof · cited by 1
- CategoryTheory.Under.mapPushoutAdj_counit_appstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.pushoutMapstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.Under.pushoutCompForgetIso_hom_app_rightstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.Under.pushoutCompForgetIso_inv_app_rightstatement and proof · cited by 0
- CategoryTheory.Under.pushoutCompstatement and proof · cited by 0
- CategoryTheory.Under.pushout.congr_simpstatement and proof · cited by 0