Theorems · Definition · nonassociative algebras
RootPairing.toLinearMap
{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] → RootPairing ι R M N → M →ₗ[R] N →ₗ[R] R- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 108 results in Mathlib
- Foundations
- Depth 32 from the axioms, rests on 364 definitions · uses propext, Quot.sound
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.
- 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
- LinearMapstatement · cited by 10,215
- RootPairingstatement and proof · cited by 710
Cited by122
Results whose statement or proof uses this declaration.
- RootPairing.flipproof · cited by 79
- RootPairing.ne_zeroproof · cited by 32
- RootPairing.coroot'proof · cited by 32
- RootPairing.root'proof · cited by 19
- RootPairing.rootForm_symmetricproof · cited by 11
- RootPairing.rootForm_apply_applyproof · cited by 10
- RootPairing.Polarization_applyproof · cited by 8
- RootPairing.root_sub_root_mem_of_pairingIn_posproof · cited by 7
- RootPairing.Equiv.extproof · cited by 7
- RootPairing.coroot_root_twostatement · cited by 7
- RootPairing.Hom.extproof · cited by 6
- RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRedproof · cited by 6