I work with a category in which every object $A$ is a finite copower of an object $x$, i.e. $A$ is of the form $$x\coprod x\coprod\cdots\coprod x.$$ Moreover, I know that this category has finite colimits. If I take its idempotent completion, do I get finite limits too?
I am almost sure I do, but I am a bit confused at the moment. Any advice would be appreciated. Thanks.