Theorems · Theorem · ring theory
CliffordAlgebra.submodule_map_involute_eq_comap
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
(Q : QuadraticForm R M) (p : Submodule R (CliffordAlgebra Q)),
Submodule.map CliffordAlgebra.involute.toLinearMap p = Submodule.comap CliffordAlgebra.involute.toLinearMap p- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Submodulestatement and proof · cited by 7,192
- Submodule.mapstatement · cited by 614
- QuadraticFormstatement and proof · cited by 507
- Submodule.comapstatement · cited by 347
- CliffordAlgebrastatement and proof · cited by 309
- AlgHom.toLinearMapstatement · cited by 254
- AlgEquiv.toLinearEquivproof · cited by 117
- CliffordAlgebra.involutestatement · cited by 36
Cited by2
Results whose statement or proof uses this declaration.
- CliffordAlgebra.evenOdd_comap_involuteproof · cited by 1
- CliffordAlgebra.ι_range_comap_involuteproof · cited by 0