English
The inclusion map inl: G₀ →*₀ WithZero (G₀ˣ × H₀ˣ) is a monoid-with-zero hom extending the unit structure via units.
Русский
Включение inl: G₀ →*₀ WithZero (G₀ˣ × H₀ˣ) образует монодную с нулём гомоморфизм, расширяющий структуру единицы через единицы.
LaTeX
$$$\text{inl} : G_0 \to^*_0 WithZero (G_0^× × H_0^×)$$$
Lean4
/-- Given groups with zero `G₀`, `H₀`, the natural inclusion ordered homomorphism from
`G₀` to `WithZero (G₀ˣ × H₀ˣ)`, which is the group with zero that can be identified
as their product. -/
def inl [DecidablePred fun x : G₀ ↦ x = 0] : G₀ →*₀ WithZero (G₀ˣ × H₀ˣ) :=
(WithZero.map' (.inl _ _)).comp (MonoidWithZeroHomClass.toMonoidWithZeroHom WithZero.withZeroUnitsEquiv.symm)
