opProductIsoCoproduct — Mathlib

English

The canonical isomorphism from op of a product to the coproduct in the opposite category is natural with respect to the limit and colimit structures.

Русский

Канонический изоморфизм из Opposite(пользуется произведением) в копродукт в противоположной категории естественен относительно структур предела и колимита.

LaTeX

$$$opProductIsoCoproduct' (hf, hc) : op(\prod Z) \cong \coprod (op Z)$ is natural in $(hf, hc)$$$

Lean4

/-- The canonical isomorphism from the opposite of the product to the coproduct in the opposite
category.
-/
def opProductIsoCoproduct : op (∏ᶜ Z) ≅ ∐ (op <| Z ·) :=
  opProductIsoCoproduct' (productIsProduct Z) (coproductIsCoproduct (op <| Z ·))

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