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Theorems · Inductive type · category theory

CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlong

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → {X Y : C} → (X ⟶ Y) → Prop

P.IsStableUnderCobaseChangeAlong f states that for any morphism satisfying P with the same codomain as f, any pullback of that morphism along f also satisfies P.

Defined in
Mathlib.CategoryTheory.MorphismProperty.Limits
Cited by
16 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.

CategoryTheory.MorphismProperty.Under.pushout · cited by 15Under.pushoutCategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlong.of_isPushout · cited by 4IsStableUnderCobaseChange…CategoryTheory.MorphismProperty.Under.pushoutCompForgetIso · cited by 4Under.pushoutCompForgetIsoCategoryTheory.MorphismProperty.Under.mapPushoutAdj · cited by 3Under.mapPushoutAdjCategoryTheory.MorphismProperty.Under.pushoutComp · cited by 2Under.pushoutCompCategoryTheory.MorphismProperty.Under.pushoutCongr · cited by 2Under.pushoutCongrCategoryTheory.MorphismProperty.pushout_inl · cited by 1MorphismProperty.pushout_…CategoryTheory.MorphismProperty.pushout_inr · cited by 1MorphismProperty.pushout_…CategoryTheory.MorphismProperty.Under.pushoutCongr_hom_app_left_fst · cited by 1Under.pushoutCongr_hom_ap…CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAgainst.casesOn · cited by 0IsStableUnderCobaseChange…CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAgainst.isStableUnderCobaseChangeAlong · cited by 0IsStableUnderCobaseChange…CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAgainst.recOn · cited by 0IsStableUnderCobaseChange…CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlong.casesOn · cited by 0IsStableUnderCobaseChange…CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlong.recOn · cited by 0IsStableUnderCobaseChange…CategoryTheory.MorphismProperty.isLeftAdjoint_pushout · cited by 0MorphismProperty.isLeftAd…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…MorphismProperty.IsStableUnde…CITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by25

Results whose statement or proof uses this declaration.