Learn Swedish: Den här kategorin innehåller sysselsatta personer.

In Swedish, demonstrative pronouns like den här (this) and den där (that) must be followed by the noun in its definite form. So, you need both the article den and the definite suffix -n at the end of kategori, creating the standard "double definite" structure: den här kategorin.

What form of the word is sysselsatta here?

It is the past participle of the verb sysselsätta (to employ or keep busy). Here, it acts as an adjective describing personer. Because personer is plural, the participle must take the plural ending -a, becoming sysselsatta.

How would I add "of whom half are women" to this sentence using this lesson's focus word, varav?

You would add a comma and then use varav to refer back to the group of personer, like this: Den här kategorin innehåller sysselsatta personer, varav hälften är kvinnor. The word varav acts as a formal way to say "of which" or "of whom" when you want to describe a specific subset of the group you just mentioned.

I often mix up innehåller and innebär. Why is it innehåller here?