Theorems · Theorem · category theory
Quiver.FreeGroupoid.congr_reverse_comp
∀ {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 (Quiver.Path.reverse p) p) =
Quot.mk (CategoryTheory.HomRel.CompClosure Quiver.FreeGroupoid.redStep) (CategoryTheory.CategoryStruct.id Y)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- Quiver
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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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- Quiverstatement and proof · cited by 405
- Quiver.Pathproof · cited by 166
- CategoryTheory.Pathsstatement and proof · cited by 82
- Quiver.Symmetrifystatement and proof · cited by 28
- CategoryTheory.HomRel.CompClosurestatement and proof · cited by 19
- Quiver.Path.reversestatement and proof · cited by 7
- Quiver.FreeGroupoid.redStepstatement and proof · cited by 7
- Quiver.Path.reverse_reverseproof · cited by 1
- Quiver.FreeGroupoid.congr_comp_reverseproof · cited by 1
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