Theorems · Theorem · nonassociative algebras
RootPairing.Equiv.reflection_coweightEquiv
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
[inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : RootPairing ι R M N) (i : ι),
RootPairing.Equiv.coweightEquiv P P (RootPairing.Equiv.reflection P i) = P.coreflection i- Defined in
- Mathlib.LinearAlgebra.RootSystem.Hom
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearEquivstatement · cited by 3,317
- RootPairingstatement and proof · cited by 710
- RootPairing.coreflectionstatement · cited by 28
- RootPairing.Equiv.reflectionstatement · cited by 15
- LinearEquiv.toLinearMap_injproof · cited by 14
- RootPairing.Equiv.coweightEquivstatement · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.Equiv.reflection_invproof · cited by 5
- RootPairing.range_weylGroup_coweightHomproof · cited by 0