Theorems · Theorem · nonassociative algebras
RootPairing.algebraMap_coxeterWeightIn
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} {N : Type u_5} [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) (S : Type u_7)
[inst_5 : CommRing S] [inst_6 : Algebra S R] [inst_7 : P.IsValuedIn S] (i j : ι),
(algebraMap S R) (P.coxeterWeightIn S i j) = P.coxeterWeight i j- Cited by
- 3 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- map_mulproof · cited by 1,137
- RootPairingstatement and proof · cited by 710
- RootPairing.IsValuedInstatement and proof · cited by 108
- RootPairing.pairingInproof · cited by 100
- RootPairing.pairingproof · cited by 88
Cited by3
Results whose statement or proof uses this declaration.
- RootPairing.linearIndependent_iff_coxeterWeightIn_ne_fourproof · cited by 3
- RootPairing.coxeterWeightIn_eq_zero_iffproof · cited by 1
- RootPairing.coxeterWeightIn_le_fourproof · cited by 1