Theorems · Definition · combinatorics
Quiver.symmetrifyCostar
{U : Type u_1} →
[inst : Quiver U] → (u : U) → Quiver.Costar (Quiver.Symmetrify.of.obj u) ≃ Quiver.Costar u ⊕ Quiver.Star uThe costar of the symmetrification of a quiver at a vertex u is equivalent to the sum of the
costar and the star at u in the original quiver.
- Defined in
- Mathlib.Combinatorics.Quiver.Covering
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- Equivstatement · cited by 8,337
- Prefunctor.objstatement and proof · cited by 1,241
- Quiverstatement and proof · cited by 405
- Quiver.Symmetrifystatement and proof · cited by 28
- Quiver.Starstatement · cited by 22
- Quiver.Costarstatement · cited by 19
- Quiver.Symmetrify.ofstatement and proof · cited by 9
- Equiv.sigmaSumDistribproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Prefunctor.symmetrifyCostarstatement and proof · cited by 1
- Prefunctor.IsCovering.symmetrifyproof · cited by 0