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Theorems · Theorem · category theory

SemimoduleCat.MonoidalCategory.id_tensorHom_id

∀ {R : Type u} [inst : CommSemiring R] (M : SemimoduleCat R) (N : SemimoduleCat R),
  SemimoduleCat.MonoidalCategory.tensorHom (CategoryTheory.CategoryStruct.id M) (CategoryTheory.CategoryStruct.id N) =
    CategoryTheory.CategoryStruct.id (SemimoduleCat.of R (TensorProduct R ↑M ↑N))
Defined in
Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
Cited by
0 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Quot.sound
Assumes
CommSemiring
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Quiver.Hom · cited by 32603Quiver.HomCommSemiring · cited by 10911CommSemiringCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idTensorProduct · cited by 2545TensorProductTensorProduct.mk · cited by 129TensorProduct.mkSemimoduleCat · cited by 108SemimoduleCatSemimoduleCat.carrier · cited by 87SemimoduleCat.carrierTensorProduct.ext · cited by 50TensorProduct.extSemimoduleCat.Hom.hom · cited by 45Hom.homSemimoduleCat.of · cited by 25SemimoduleCat.ofLinearMap.compr₂ₛₗ · cited by 25LinearMap.compr₂ₛₗSemimoduleCat.hom_ext · cited by 15SemimoduleCat.hom_extSemimoduleCat.MonoidalCategory.tensorObj · cited by 12MonoidalCategory.tensorObjSemimoduleCat.MonoidalCategory.tensorHom · cited by 7MonoidalCategory.tensorHomMonoidalCategory.id_tensorHom…CITED BYCITES

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