instAddCommGroupWithOne — Mathlib

English

The left and right inclusions are compatible with the algebra maps from R, i.e., (algebraMap_R_A) ∘ includeLeft = (algebraMap_R_B) ∘ includeRight.

Русский

Левые и правые включения совместимы с алгебраобразованиями из R: алгебраMap_R_A ∘ includeLeft = алгебраMap_R_B ∘ includeRight.

LaTeX

$$$\text{algebraMap}_A\circ i_L = \text{algebraMap}_B\circ i_R$ as maps R → A ⊗_R B.$$

Lean4

instance instAddCommGroupWithOne : AddCommGroupWithOne (A ⊗[R] B)
    where
  toAddCommGroup := TensorProduct.addCommGroup
  __ := instAddCommMonoidWithOne
  intCast z := z ⊗ₜ (1 : B)
  intCast_ofNat n := by simp [natCast_def]
  intCast_negSucc n := by simp [natCast_def, add_tmul, neg_tmul, one_def]

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