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Theorems · Theorem · commutative algebra

Algebra.TensorProduct.linearEquivIncludeRange_toLinearMap

∀ (R : Type u_1) (S : Type u_2) (T : Type u_3) [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S]
  [inst_3 : Semiring T] [inst_4 : Algebra R T],
  ↑(Algebra.TensorProduct.linearEquivIncludeRange R S T) =
    TensorProduct.map Algebra.TensorProduct.includeLeft.toLinearMap.rangeRestrict
      Algebra.TensorProduct.includeRight.toLinearMap.rangeRestrict
Defined in
Mathlib.LinearAlgebra.TensorProduct.Subalgebra
Cited by
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Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringSemiringAlgebraSemiringAlgebra
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RingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapSubmodule · cited by 7192SubmoduleTensorProduct · cited by 2545TensorProductSubalgebra · cited by 1353SubalgebraLinearEquiv.toLinearMap · cited by 1171LinearEquiv.toLinearMapLinearMap.range · cited by 893LinearMap.rangeAlgHom.toLinearMap · cited by 254AlgHom.toLinearMapTensorProduct.map · cited by 250TensorProduct.mapAlgHom.range · cited by 169AlgHom.rangeAlgebra.TensorProduct.includeRight · cited by 165TensorProduct.includeRightAlgebra.TensorProduct.includeLeft · cited by 72TensorProduct.includeLeftTensorProduct.linearEquivIncl…CITED BYCITES

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