Theorems · Definition · combinatorics
Quiver.starEquivCostar
{U : Type u_1} → [inst : Quiver U] → [Quiver.HasInvolutiveReverse U] → (u : U) → Quiver.Star u ≃ Quiver.Costar uIn a quiver with involutive inverses, the star and costar at every vertex are equivalent.
This map is induced by Quiver.reverse.
- Defined in
- Mathlib.Combinatorics.Quiver.Covering
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
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.
- Equivstatement · cited by 8,337
- Quiverstatement and proof · cited by 405
- Quiver.reverseproof · cited by 23
- Quiver.Starstatement and proof · cited by 22
- Quiver.Costarstatement and proof · cited by 19
- Quiver.HasInvolutiveReversestatement and proof · cited by 17
Cited by8
Results whose statement or proof uses this declaration.
- Prefunctor.bijective_costar_iff_bijective_starproof · cited by 2
- Prefunctor.costar_conj_starstatement and proof · cited by 1
- Quiver.starEquivCostar_apply_sndstatement and proof · cited by 0
- Quiver.starEquivCostar_symm_applystatement · cited by 0
- Quiver.starEquivCostar_symm_apply_fststatement and proof · cited by 0
- Quiver.starEquivCostar_symm_apply_sndstatement and proof · cited by 0
- Quiver.starEquivCostar_applystatement · cited by 0
- Quiver.starEquivCostar_apply_fststatement and proof · cited by 0