prodMap — Mathlib

English

The coproduct (joint codomain) of two continuous homomorphisms to a common codomain is obtained by composing multiplication with the product map.

Русский

Копрод — это совместное отображение в общий кодомоморфизм через умножение совместно с произведением.

LaTeX

$$$f.coprod g = (mul_E).comp (f.prodMap g)$$$

Lean4

/-- Product of two continuous homomorphisms on different spaces. -/
@[to_additive (attr := simps!) prodMap /-- Product of two continuous homomorphisms on different spaces. -/
    ]
def prodMap (f : A →ₜ* C) (g : B →ₜ* D) : (A × B) →ₜ* (C × D) :=
  ⟨f.toMonoidHom.prodMap g.toMonoidHom, f.continuous_toFun.prodMap g.continuous_toFun⟩

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