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Theorems · Definition · category theory

CategoryTheory.Cat.FreeRefl.induction

{V : Type u_1} →
  [inst : CategoryTheory.ReflQuiver V] →
    {motive : CategoryTheory.Cat.FreeRefl V → Sort u_2} →
      ((v : V) → motive (CategoryTheory.Cat.FreeRefl.mk v)) → (x : CategoryTheory.Cat.FreeRefl V) → motive x

Induction principle for the objects of the free category on a reflexive quiver.

Defined in
Mathlib.CategoryTheory.Category.ReflQuiv
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.ReflQuiver
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CategoryTheory.Cat.FreeRefl.hom_induction · cited by 1FreeRefl.hom_inductionCategoryTheory.ReflQuiver · cited by 64CategoryTheory.ReflQuiverCategoryTheory.Quotient.as · cited by 47Quotient.asCategoryTheory.Cat.FreeRefl · cited by 34Cat.FreeReflCategoryTheory.Cat.FreeRefl.mk · cited by 17FreeRefl.mkFreeRefl.inductionCITED BYCITES

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