Theorems · Definition · category theory

CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAgainst.recOn

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {P P' : CategoryTheory.MorphismProperty C} →
      {motive : P.IsStableUnderCobaseChangeAgainst P' → Sort u_1} →
        (t : P.IsStableUnderCobaseChangeAgainst P') →
          ((isStableUnderCobaseChangeAlong : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), P' f → P.IsStableUnderCobaseChangeAlong f) →
              motive ⋯) →
            motive t

Defined in: Mathlib.CategoryTheory.MorphismProperty.Limits
Cited by: 0 results in Mathlib
Foundations: Depth 6 from the axioms · uses no axioms
Assumes: CategoryTheory.Category

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlongstatement and proof · cited by 16
CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAgainststatement and proof · cited by 2

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