Theorems · Inductive type · category theory

CategoryTheory.MorphismProperty.multiplicativeClosure.below

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {W : CategoryTheory.MorphismProperty C} →
      {motive : ⦃X Y : C⦄ → (x : X ⟶ Y) → W.multiplicativeClosure x → Prop} →
        {X Y : C} → {x : X ⟶ Y} → W.multiplicativeClosure x → Prop

Defined in: Mathlib.CategoryTheory.MorphismProperty.Composition
Cited by: 1 results in Mathlib
Foundations: Depth 4 from the axioms · uses no axioms
Assumes: CategoryTheory.Category

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Cites4

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
CategoryTheory.MorphismProperty.multiplicativeClosurestatement · cited by 18

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.multiplicativeClosure.below.casesOnstatement and proof · cited by 0
CategoryTheory.MorphismProperty.multiplicativeClosure.brecOnstatement and proof · cited by 0