Theorems · Definition · category theory

CategoryTheory.MorphismProperty.HasPushoutsAlong.recOn

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {P : CategoryTheory.MorphismProperty C} →
      {X Y : C} →
        {f : X ⟶ Y} →
          {motive : P.HasPushoutsAlong f → Sort u_1} →
            (t : P.HasPushoutsAlong f) →
              ((hasPushout : ∀ {W : C} (g : X ⟶ W), P g → CategoryTheory.Limits.HasPushout g f) → motive ⋯) → motive t

Defined in: Mathlib.CategoryTheory.MorphismProperty.Limits
Cited by: 0 results in Mathlib
Foundations: Depth 20 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.Limits.HasPushoutstatement and proof · cited by 192
CategoryTheory.MorphismProperty.HasPushoutsAlongstatement and proof · cited by 12

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