Theorems · Definition · commutative algebra
LinearEquiv.neg
(R : Type u_1) → {M : Type u_5} → [inst : Semiring R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → M ≃ₗ[R] Mx ↦ -x as a LinearEquiv
- Defined in
- Mathlib.Algebra.Module.Equiv.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- LinearEquivstatement · cited by 3,317
- Equiv.Permproof · cited by 1,375
- LinearMap.idproof · cited by 625
- Equiv.toFunproof · cited by 279
- Equiv.invFunproof · cited by 163
- Equiv.right_invproof · cited by 68
- Equiv.left_invproof · cited by 59
Cited by10
Results whose statement or proof uses this declaration.
- LinearIsometryEquiv.negproof · cited by 14
- ContinuousLinearEquiv.negproof · cited by 11
- AffineEquiv.constVSubproof · cited by 8
- LieAlgebra.Basis.symm_baseSuppproof · cited by 2
- IsModuleTopology.continuous_negproof · cited by 1
- Module.Basis.span_negstatement and proof · cited by 1
- LinearEquiv.symm_negstatement · cited by 0
- LinearEquiv.coe_negstatement · cited by 0
- LinearEquiv.neg_applystatement · cited by 0
- AffineEquiv.linear_constVSubstatement · cited by 0