Theorems · Theorem · commutative algebra
Module.Invertible.lTensor_surjective_iff
∀ {R : Type u} (M : Type v) {N : Type u_1} {P : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : Module R M] [inst_5 : Module R N]
[inst_6 : Module R P] [Module.Invertible R M] {f : N →ₗ[R] P},
Function.Surjective ⇑(LinearMap.lTensor M f) ↔ Function.Surjective ⇑f- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- TensorProductstatement · cited by 2,545
- LinearEquiv.symmproof · cited by 1,461
- Module.Dualproof · cited by 583
- LinearEquiv.transproof · cited by 298
- LinearMap.lTensorstatement and proof · cited by 203
- TensorProduct.lidproof · cited by 96
Cited by1
Results whose statement or proof uses this declaration.
- Module.Invertible.rTensor_surjective_iffproof · cited by 0