Theorems · Theorem · ring theory
TensorAlgebra.toDirectSum_comp_ofDirectSum
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
TensorAlgebra.toDirectSum.comp TensorAlgebra.ofDirectSum = AlgHom.id R (DirectSum ℕ fun n => TensorPower R n M)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement · cited by 3,236
- AlgHom.compstatement · cited by 501
- DirectSumstatement · cited by 446
- AlgHom.idstatement · cited by 196
- DirectSum.ofproof · cited by 122
- PiTensorProduct.tprodproof · cited by 117
- TensorAlgebrastatement · cited by 81
- MultilinearMap.extproof · cited by 60
Cited by2
Results whose statement or proof uses this declaration.
- TensorAlgebra.equivDirectSumproof · cited by 2
- TensorAlgebra.toDirectSum_ofDirectSumproof · cited by 0