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Theorems · Inductive type · category theory

Quiver.FreeGroupoid.redStep

{V : Type u} → [inst : Quiver V] → HomRel (CategoryTheory.Paths (Quiver.Symmetrify V))

The "reduction" relation

Defined in
Mathlib.CategoryTheory.Groupoid.FreeGroupoid
Cited by
7 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
Quiver
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Quiver.FreeGroupoid · cited by 8Quiver.FreeGroupoidQuiver.FreeGroupoid.of · cited by 7FreeGroupoid.ofQuiver.FreeGroupoid.lift · cited by 5FreeGroupoid.liftQuiver.FreeGroupoid.lift_unique · cited by 3FreeGroupoid.lift_uniqueQuiver.FreeGroupoid.congr_comp_reverse · cited by 1FreeGroupoid.congr_comp_r…Quiver.FreeGroupoid.lift_spec · cited by 1FreeGroupoid.lift_specQuiver.FreeGroupoid.of_eq · cited by 1FreeGroupoid.of_eqQuiver.FreeGroupoid.redStep.casesOn · cited by 1redStep.casesOnCategoryTheory.FreeGroupoid.eq_mk · cited by 0FreeGroupoid.eq_mkQuiver.FreeGroupoid.congr_reverse · cited by 0FreeGroupoid.congr_reverseQuiver.FreeGroupoid.congr_reverse_comp · cited by 0FreeGroupoid.congr_revers…Quiver.FreeGroupoid.quotInv · cited by 0FreeGroupoid.quotInvQuiver.FreeGroupoid.redStep.recOn · cited by 0redStep.recOnQuiver · cited by 405QuiverCategoryTheory.Paths · cited by 82CategoryTheory.PathsHomRel · cited by 49HomRelQuiver.Symmetrify · cited by 28Quiver.SymmetrifyFreeGroupoid.redStepCITED BYCITES

Cites4

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

Cited by13

Results whose statement or proof uses this declaration.