Theorems · Theorem · commutative algebra
IsTensorProduct.map_id
∀ {R : Type u_1} [inst : CommSemiring R] {M₁ : Type u_2} {M₂ : Type u_3} {M : Type u_4} [inst_1 : AddCommMonoid M₁]
[inst_2 : AddCommMonoid M₂] [inst_3 : AddCommMonoid M] [inst_4 : Module R M₁] [inst_5 : Module R M₂]
[inst_6 : Module R M] {f : M₁ →ₗ[R] M₂ →ₗ[R] M} (hf : IsTensorProduct f),
hf.map hf LinearMap.id LinearMap.id = LinearMap.id- Defined in
- Mathlib.RingTheory.IsTensorProduct
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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 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
- map_zeroproof · cited by 1,614
- map_addproof · cited by 964
- LinearMap.extproof · cited by 844
- LinearMap.idstatement and proof · cited by 625
- IsTensorProductstatement and proof · cited by 31
- IsTensorProduct.mapstatement and proof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- IsTensorProduct.map_oneproof · cited by 1