Theorems · Definition · linear algebra
exteriorPower.zeroEquiv
(R : Type u) → [inst : CommRing R] → (M : Type u_1) → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → ↥(⋀[R]^0 M) ≃ₗ[R] R
The linear equivalence ⋀[R]^0 M ≃ₗ[R] R.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 99 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.
- DFunLike.coeproof · cited by 62,936
- 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 · cited by 7,192
- LinearEquivstatement · cited by 3,317
- QuadraticFormstatement · cited by 507
- ExteriorAlgebrastatement · cited by 131
- ExteriorAlgebra.exteriorPowerstatement · cited by 66
- exteriorPower.ιMultiproof · cited by 30
- AlternatingMap.constOfIsEmptyproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- ModuleCat.exteriorPower.iso₀proof · cited by 3
- exteriorPower.zeroEquiv_ιMultistatement · cited by 2
- exteriorPower.zeroEquiv_naturalitystatement and proof · cited by 1
- exteriorPower.zeroEquiv_symm_applystatement and proof · cited by 0