Theorems · Theorem · ring theory
CliffordAlgebra.hom_ext
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{Q : QuadraticForm R M} {A : Type u_4} [inst_3 : Semiring A] [inst_4 : Algebra R A] {f g : CliffordAlgebra Q →ₐ[R] A},
f.toLinearMap ∘ₗ CliffordAlgebra.ι Q = g.toLinearMap ∘ₗ CliffordAlgebra.ι Q → f = gSee note [partially-applied ext lemmas].
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement and proof · cited by 10,215
- Algebra.algebraMapproof · cited by 4,706
- Equiv.symmproof · cited by 3,681
- AlgHomstatement and proof · cited by 3,236
- LinearMap.compstatement and proof · cited by 1,642
Cited by17
Results whose statement or proof uses this declaration.
- CliffordAlgebra.inductionproof · cited by 8
- CliffordAlgebra.map_comp_mapproof · cited by 3
- CliffordAlgebra.map_idproof · cited by 3
- ExteriorAlgebra.hom_extproof · cited by 2
- CliffordAlgebraComplex.ofComplex_comp_toComplexproof · cited by 1
- CliffordAlgebra.involute_comp_involuteproof · cited by 1
- CliffordAlgebraComplex.toComplex_involuteproof · cited by 1
- CliffordAlgebraQuaternion.ofQuaternion_comp_toQuaternionproof · cited by 1
- CliffordAlgebra.toBaseChange_comp_ofBaseChangeproof · cited by 1
- CliffordAlgebra.toBaseChange_comp_involuteproof · cited by 1
- CliffordAlgebra.toBaseChange_comp_reverseOpproof · cited by 1
- CliffordAlgebra.ofBaseChange_comp_toBaseChangeproof · cited by 1