Yes. And they are living in the UK. We're both right.
A monarchy is an abstract system instantiated within the country to which it applies.
The monarchy of Canada does not reside in the UK .. perhaps you're thinking of the current appointed monarch.
> The monarchy of Canada is the monarchy in the UK.
is false.
As it so happens for the moment.
It's not a bound requirement that such be the case .. as any true student of the history of Wales, Scotland, Northern Ireland, England, and the Union would well be aware of.