Theorems · Definition · category theory
CategoryTheory.Cat.FreeRefl
(V : Type u_1) → [CategoryTheory.ReflQuiver V] → Type u_1
A reflexive quiver generates a free category, defined as a quotient of the free category on its underlying quiver (called the "path category") by the hom relation that uses the specified reflexivity arrows as the identity arrows.
- Defined in
- Mathlib.CategoryTheory.Category.ReflQuiv
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- CategoryTheory.ReflQuiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.ReflQuiverstatement and proof · cited by 64
- CategoryTheory.Quotientproof · cited by 48
- CategoryTheory.Cat.FreeReflRelproof · cited by 4
Cited by49
Results whose statement or proof uses this declaration.
- CategoryTheory.Cat.FreeRefl.mkstatement · cited by 17
- CategoryTheory.Cat.FreeRefl.homMkstatement · cited by 13
- CategoryTheory.Cat.freeReflproof · cited by 8
- CategoryTheory.Cat.FreeRefl.quotientFunctorstatement · cited by 8
- CategoryTheory.Cat.FreeRefl.liftstatement · cited by 6
- CategoryTheory.Cat.freeReflMapstatement · cited by 5
- SSet.Truncated.HomotopyCategory.quotientFunctorstatement · cited by 5
- CategoryTheory.ReflQuiv.adj.homEquivstatement and proof · cited by 5
- CategoryTheory.Cat.toFreeReflstatement · cited by 5
- CategoryTheory.Cat.FreeRefl.morphismPropertyHomMkstatement · cited by 5
- CategoryTheory.Cat.FreeRefl.lift_mapstatement · cited by 4
- SSet.OneTruncation₂.HoRel₂statement · cited by 3