Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.HasPullbacksAlong
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → {X Y : C} → (X ⟶ Y) → PropP.HasPullbacksAlong f states that for any morphism satisfying P with the same codomain
as f, the pullback of that morphism along f exists.
- Cited by
- 17 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.MorphismPropertystatement · cited by 2,179
Cited by25
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.Over.pullbackstatement and proof · cited by 42
- CategoryTheory.MorphismProperty.Over.mapPullbackAdjstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.Over.pullbackCompstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.Over.pullbackCongrstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.HasPullbacksAlong.hasPullbackstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fststatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.fst_gluedCocone_ιproof · cited by 1
- CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_appstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_appstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.isRightAdjoint_pullbackstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_leftstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_leftstatement and proof · cited by 0