Theorems · Theorem · commutative algebra
TensorProduct.congr_refl_refl
∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_7} {N : Type u_8} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N],
TensorProduct.congr (LinearEquiv.refl R M) (LinearEquiv.refl R N) = LinearEquiv.refl R (TensorProduct R M N)- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Map
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- LinearEquivstatement · cited by 3,317
- TensorProductstatement and proof · cited by 2,545
- LinearEquiv.reflstatement and proof · cited by 143
- TensorProduct.congrstatement and proof · cited by 50
- TensorProduct.ext'proof · cited by 39
- LinearEquiv.toLinearMap_injectiveproof · cited by 29
Cited by4
Results whose statement or proof uses this declaration.
- TensorProduct.congr_powproof · cited by 3
- LinearEquiv.lTensor_reflproof · cited by 1
- LinearEquiv.rTensor_reflproof · cited by 1
- TensorProduct.congrIsometry_refl_reflproof · cited by 0