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Theorems · Definition · nonassociative algebras

LieHom.fst

(R : Type u_1) →
  (L₁ : Type u_2) →
    (L₂ : Type u_3) →
      [inst : CommRing R] →
        [inst_1 : LieRing L₁] →
          [inst_2 : LieAlgebra R L₁] → [inst_3 : LieRing L₂] → [inst_4 : LieAlgebra R L₂] → L₁ × L₂ →ₗ⁅R⁆ L₁

The first projection of a product is a Lie algebra map.

Defined in
Mathlib.Algebra.Lie.Prod
Cited by
9 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Quot.sound
Assumes
CommRingLieRingLieAlgebraLieRingLieAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LieHom.prodMap · cited by 6LieHom.prodMapLieHom.range_inr · cited by 1LieHom.range_inrLieHom.fst_apply · cited by 0LieHom.fst_applyLieHom.fst_comp_inl · cited by 0LieHom.fst_comp_inlLieHom.fst_comp_inr · cited by 0LieHom.fst_comp_inrLieHom.fst_prod · cited by 0LieHom.fst_prodLieHom.fst_surjective · cited by 0LieHom.fst_surjectiveLieHom.ker_fst · cited by 0LieHom.ker_fstLieHom.coe_fst · cited by 0LieHom.coe_fstLieHom.pair_fst_snd · cited by 0LieHom.pair_fst_sndRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingLinearMap · cited by 10215LinearMapLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieHom · cited by 382LieHomLinearMap.fst · cited by 64LinearMap.fstLieHom.fstCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by10

Results whose statement or proof uses this declaration.