Theorems · Theorem · category theory
CategoryTheory.Cat.FreeRefl.quotientFunctor_map_id
∀ (V : Type u_2) [inst : CategoryTheory.ReflQuiver V] (X : V),
(CategoryTheory.Cat.FreeRefl.quotientFunctor V).map (CategoryTheory.ReflQuiver.id X).toPath =
CategoryTheory.CategoryStruct.id ((CategoryTheory.Cat.FreeRefl.quotientFunctor V).obj X)- Defined in
- Mathlib.CategoryTheory.Category.ReflQuiv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.ReflQuiver
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Pathsstatement · cited by 82
- CategoryTheory.ReflQuiverstatement and proof · cited by 64
- Quiver.Hom.toPathstatement · cited by 38
- CategoryTheory.Cat.FreeReflstatement · cited by 34
- CategoryTheory.ReflQuiver.idstatement · cited by 18
- CategoryTheory.Quotient.soundproof · cited by 16
- CategoryTheory.Cat.FreeRefl.quotientFunctorstatement · cited by 8
- CategoryTheory.Cat.FreeReflRelproof · cited by 4
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