Theorems · Definition · category theory
CategoryTheory.Cat.FreeRefl.quotientFunctor
(V : Type u_1) → [inst : CategoryTheory.ReflQuiver V] → CategoryTheory.Functor (CategoryTheory.Paths V) (CategoryTheory.Cat.FreeRefl V)
The quotient functor associated to a quotient category defines a natural map from the free category on the underlying quiver of a refl quiver to the free category on the reflexive quiver.
- Defined in
- Mathlib.CategoryTheory.Category.ReflQuiv
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.ReflQuiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Pathsstatement · cited by 82
- CategoryTheory.ReflQuiverstatement and proof · cited by 64
- CategoryTheory.Quotient.functorproof · cited by 41
- CategoryTheory.Cat.FreeReflstatement · cited by 34
- CategoryTheory.Cat.FreeReflRelproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.Cat.FreeRefl.homMkproof · cited by 13
- CategoryTheory.Cat.FreeRefl.lift_unique'statement and proof · cited by 1
- CategoryTheory.Cat.FreeRefl.hom_inductionproof · cited by 1
- SSet.OneTruncation₂.HoRel₂.casesOnstatement and proof · cited by 0
- CategoryTheory.Cat.freeReflMap_naturalitystatement and proof · cited by 0
- CategoryTheory.Cat.FreeRefl.quotientFunctor_map_consstatement · cited by 0
- CategoryTheory.Cat.FreeRefl.quotientFunctor_map_idstatement · cited by 0
- CategoryTheory.Cat.FreeRefl.quotientFunctor_map_nilstatement and proof · cited by 0
- SSet.OneTruncation₂.HoRel₂.recOnstatement and proof · cited by 0
- CategoryTheory.Cat.freeReflNatTransproof · cited by 0
- CategoryTheory.ReflQuiv.adj.counit.comp_app_eqstatement and proof · cited by 0
- CategoryTheory.ReflQuiv.adj.unit.map_app_eqstatement · cited by 0