Theorems · Theorem · category theory
CategoryTheory.Quiv.freeMap_pathsOf_pathComposition
∀ (V : Type u) [inst : Quiver V],
(CategoryTheory.Cat.freeMap (CategoryTheory.Paths.of V)).comp
(CategoryTheory.pathComposition (CategoryTheory.Paths V)) =
CategoryTheory.Functor.id (CategoryTheory.Paths V)- Defined in
- Mathlib.CategoryTheory.Category.Quiv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Quiver
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- Quiverstatement and proof · cited by 405
- CategoryTheory.Pathsstatement · cited by 82
- Quiver.Hom.toPathproof · cited by 38
- CategoryTheory.Paths.ofstatement · cited by 20
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