Theorems · Theorem · category theory

Quiver.FreeGroupoid.congr_comp_reverse

∀ {V : Type u} [inst : Quiver V] {X Y : CategoryTheory.Paths (Quiver.Symmetrify V)} (p : X ⟶ Y),
  Quot.mk (CategoryTheory.HomRel.CompClosure Quiver.FreeGroupoid.redStep)
      (CategoryTheory.CategoryStruct.comp p (Quiver.Path.reverse p)) =
    Quot.mk (CategoryTheory.HomRel.CompClosure Quiver.FreeGroupoid.redStep) (CategoryTheory.CategoryStruct.id X)

Defined in: Mathlib.CategoryTheory.Groupoid.FreeGroupoid
Cited by: 1 results in Mathlib
Foundations: Depth 15 from the axioms · uses propext, Quot.sound
Assumes: Quiver

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Cites17

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Category.id_compproof · cited by 1,998
Quiverstatement and proof · cited by 405
Quiver.Pathproof · cited by 166
CategoryTheory.Pathsstatement and proof · cited by 82
Relation.EqvGenproof · cited by 49
Quiver.Path.compproof · cited by 45
Quiver.Hom.toPathproof · cited by 38
Quiver.Symmetrifystatement and proof · cited by 28

Cited by1

Results whose statement or proof uses this declaration.

Quiver.FreeGroupoid.congr_reverse_compproof · cited by 0