Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlong
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → {X Y : C} → (X ⟶ Y) → PropP.IsStableUnderBaseChangeAlong f states that for any morphism satisfying P with the same
codomain as f, any pullback of that morphism along f also satisfies P.
- Cited by
- 24 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 by34
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.Over.pullbackstatement and proof · cited by 42
- CategoryTheory.MorphismProperty.pullback_sndstatement and proof · cited by 12
- CategoryTheory.MorphismProperty.Over.mapPullbackAdjstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.Over.pullbackCompstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.pullback_fststatement and proof · cited by 4
- CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlong.of_isPullbackstatement and proof · cited by 3
- CategoryTheory.MorphismProperty.Over.pullbackCompForgetIsostatement and proof · cited by 2
- CategoryTheory.MorphismProperty.Over.pullbackCongrstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.Over.pullbackMapHomPullbackstatement 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.baseChange_objstatement and proof · cited by 0