Theorems · Theorem · linear algebra

TensorProduct.AlgebraTensorModule.curry_apply

∀ {R : Type uR} {A : Type uA} {M : Type uM} {N : Type uN} {P : Type uP} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Algebra R A] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module A M]
  [inst_6 : IsScalarTower R A M] [inst_7 : AddCommMonoid N] [inst_8 : Module R N] [inst_9 : AddCommMonoid P]
  [inst_10 : Module R P] [inst_11 : Module A P] [inst_12 : IsScalarTower R A P] (f : TensorProduct R M N →ₗ[A] P)
  (a : M), (TensorProduct.AlgebraTensorModule.curry f) a = (TensorProduct.curry (↑R f)) a

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

121 results in Mathlib

Foundations

Depth 70 from the axioms, rests on 941 definitions · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTower