Theorems · Definition · linear algebra
Module.Dual.eval
(R : Type u_1) →
(M : Type u_3) →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → M →ₗ[R] Module.Dual R (Module.Dual R M)Maps a module M to the dual of the dual of M. See Module.erange_coe and
Module.evalEquiv.
- Defined in
- Mathlib.LinearAlgebra.Dual.Defs
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- LinearMap.idproof · cited by 625
- Module.Dualstatement · cited by 583
- LinearMap.flipproof · cited by 193
Cited by58
Results whose statement or proof uses this declaration.
- Submodule.dualCoannihilatorproof · cited by 41
- Module.IsReflexive.of_isPerfPairproof · cited by 29
- Module.evalEquivproof · cited by 14
- PointedCone.maxTensorProductproof · cited by 9
- Module.eval_apply_injectivestatement and proof · cited by 5
- Module.bijective_dual_evalstatement · cited by 4
- Module.subsingleton_dual_iffproof · cited by 2
- Module.evalEquiv_toLinearMapstatement · cited by 2
- Module.eval_kerstatement · cited by 2
- Module.Basis.eval_injectivestatement and proof · cited by 2
- Module.Dual.eval_applystatement · cited by 2
- Submodule.coe_dualCoannihilator_spanproof · cited by 2