"They are my cats."
Translation:Det er mine katte.
It could indeed also be "de", and I've just now added that translation :)
You've hit upon something that is hard (for me, at least) to explain. Danish likes to use "det" to indicate something, even if that something is in plural, or a person, for example:
- Det er min datter means it is my daughter, as something you would say when you meet some old friends on the street, and your daughter is with you -- also as an answer to a question like who is that?. But also:
- Hun er min datter meaning she is my daughter, as an answer to the question who is she?.
- Det er min stol even though it is en stol (common). So you could also say:
- Den er min stol which, to me, makes it sound very emphatic.
I guess the conclusion is, that to indicate something, the most common subject is "det" irrespective of the grammatical gender or number of what's being indicated. I'm sorry I don't have a better answer, but I'm not sure where to start looking for one!
As a supplement to your explanation, and in hopes that this might allow English speakers to better understand this, I'd like to mention that English uses a similar construction. For example, you might say "Look, it's the actor/actress/actors from that show", not changing the pronoun or verb (it's) regardless of the gender (actual, not grammatical) or number of the noun, whereas in Romance languages such as Spanish and Romanian, the verb would have to match the following noun for number, and I believe in French too (though I don't know enough French to be sure), where subject pronouns are required, they would have to match the following noun.