Theorems · Definition · category theory

CategoryTheory.MorphismProperty.multiplicativeClosure.casesOn

∀ {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}
  (t : W.multiplicativeClosure x),
  (∀ {x y : C} (f : x ⟶ y) (hf : W f), motive f ⋯) →
    (∀ (x : C), motive (CategoryTheory.CategoryStruct.id x) ⋯) →
      (∀ {x y z : C} (f : x ⟶ y) (g : y ⟶ z) (hf : W.multiplicativeClosure f) (hg : W g),
          motive (CategoryTheory.CategoryStruct.comp f g) ⋯) →
        motive x t

Defined in: Mathlib.CategoryTheory.MorphismProperty.Composition
Cited by: 1 results in Mathlib
Foundations: Depth 6 from the axioms · uses no axioms
Assumes: CategoryTheory.Category

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.MorphismProperty.multiplicativeClosurestatement and proof · cited by 18

Cited by1

Results whose statement or proof uses this declaration.

SimplexCategoryGenRel.exists_P_σ_P_δ_factorizationproof · cited by 0