Theorems · Theorem · commutative algebra
Module.Invertible.rightCancelEquiv_comp_rTensor_comp_symm
∀ {R : Type u} {M : Type v} {N : Type u_1} {P : Type u_2} {Q : Type u_3} [inst : CommSemiring R]
[inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : AddCommMonoid Q]
[inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : Module R P] [inst_8 : Module R Q]
(e : TensorProduct R M N ≃ₗ[R] R) (f : P →ₗ[R] Q),
↑(Module.Invertible.rightCancelEquiv Q e) ∘ₗ
LinearMap.rTensor N (LinearMap.rTensor M f) ∘ₗ ↑(Module.Invertible.rightCancelEquiv P e).symm =
f- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Quot.sound
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- 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
- LinearEquivstatement and proof · cited by 3,317
- TensorProductstatement and proof · cited by 2,545
- LinearMap.compstatement and proof · cited by 1,642
- LinearEquiv.symmstatement and proof · cited by 1,461
- TensorProduct.tmulproof · cited by 1,182
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
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