isPushout — Mathlib

English

Under pushout, the equivalence respects tensed pure tensors: (a ⊗ b) maps to algebraMap a times algebraMap b.

Русский

При пушауте равенство на простых тензорных базисах сохраняется: (a ⊗ b) → algebraMap(a) · algebraMap(b).

LaTeX

$$equiv_tmul (a) (b) = algebraMap _ _ a * algebraMap _ _ b$$

Lean4

instance isPushout {R S T : Type*} [CommSemiring R] [CommSemiring S] [CommSemiring T] [Algebra R S] [Algebra R T] :
    Algebra.IsPushout R S T (S ⊗[R] T) :=
  ⟨TensorProduct.isBaseChange R T S⟩

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