Theorems · Theorem · combinatorics
Prefunctor.bijective_costar_iff_bijective_star
∀ {U : Type u_1} [inst : Quiver U] {V : Type u_2} [inst_1 : Quiver V] (φ : U ⥤q V)
[inst_2 : Quiver.HasInvolutiveReverse U] [inst_3 : Quiver.HasInvolutiveReverse V] [φ.MapReverse] (u : U),
Function.Bijective (φ.costar u) ↔ Function.Bijective (φ.star u)- Defined in
- Mathlib.Combinatorics.Quiver.Covering
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equiv.symmproof · cited by 3,681
- Prefunctor.objstatement and proof · cited by 1,241
- Function.Bijectivestatement and proof · cited by 863
- Quiverstatement and proof · cited by 405
- Prefunctorstatement and proof · cited by 116
- Quiver.Starstatement · cited by 22
- Quiver.Costarstatement and proof · cited by 19
- Prefunctor.starstatement and proof · cited by 18
- Quiver.HasInvolutiveReversestatement and proof · cited by 17
- Prefunctor.costarstatement · cited by 14
- Quiver.starEquivCostarproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Prefunctor.isCovering_of_bijective_costarproof · cited by 0
- Prefunctor.isCovering_of_bijective_starproof · cited by 0