Theorems · Inductive type · category theory
CategoryTheory.ReflQuiver
Type u → Type (max u (v + 1))
A reflexive quiver extends a quiver with a specified arrow id X : X ⟶ X for each X in its
type of objects. We denote these arrows by id since categories can be understood as an extension
of refl quivers.
- Defined in
- Mathlib.Combinatorics.Quiver.ReflQuiver
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by100
Results whose statement or proof uses this declaration.
- CategoryTheory.ReflPrefunctor.toPrefunctorstatement and proof · cited by 36
- CategoryTheory.Cat.FreeReflstatement and proof · cited by 34
- CategoryTheory.ReflPrefunctorstatement · cited by 30
- CategoryTheory.ReflQuivproof · cited by 28
- CategoryTheory.ReflQuiver.idstatement and proof · cited by 18
- CategoryTheory.Cat.FreeRefl.mkstatement and proof · cited by 17
- CategoryTheory.Cat.FreeRefl.homMkstatement and proof · cited by 13
- CategoryTheory.ReflPrefunctor.compstatement and proof · cited by 11
- CategoryTheory.Cat.FreeRefl.quotientFunctorstatement and proof · cited by 8
- CategoryTheory.ReflPrefunctor.idstatement and proof · cited by 7
- CategoryTheory.Cat.FreeRefl.liftstatement and proof · cited by 6
- CategoryTheory.ReflQuiv.ofstatement and proof · cited by 6