No. "Sind" is present tense, "welcomed" appears only in present perfect, past tense, past perfect and future perfect (cf. http://www.wordchamp.com/lingua2/Verb.do?text=to%20welcome&languageID=13).
If the original sentence was "Deine Katzen waren willkommen" the translation would be "your cats were welcomed."
You gotta ask yourself: what is in plural in this sentence? The person you're talking to or the cats you're talking about? You are addressing a single person here (deine, which is singular). The cats are in plural. "Eure Katzen sind willkommen." translates to exactly the same English sentence, because "you" can refer to a single or many persons, but "Eure" is clearly plural. You're addressing two or more people when using "eure."
Well, here we have a compound verb "willkommen sein" = "to be welcome". So, the conjugated verb really is "sein":
Ich bin willkommen.
Du bist willkommen.
Er/Sie/Es ist willkommen.
Wir sind willkommen.
Ihr seid willkommen.
Sie sind willkommen.
So, "willkommen" never changes, "to be" does.
Now I understand where the confusion is coming from and why so many people don't get it.
Ok, guys, this is what's called a "false friend".
DO NOT, I repeat: DO NOT translate this literally into English.
"Du bist willkommen" does NOT mean "you're welcome".
It actually means someone is welcome in someone's home, or is welcome to come to a gathering or something of that sort.
"You're welcome" means "bitte" or "bitteschön" in German.
For usage hints on this sentence please read elsewhere in this thread.
There is no formal address used here. "Du"/"Deine" is informal. However, it wouldn't make a difference anyway. The sentence would read "Ihre Katzen sind willkommen." - "Ihre" being the formal address.
If we isolate just the subject and predicate of the sentence, we get "Katzen sind." - "Cats are." Whether your (informal) cats ("Deine Katzen sind.") or your (formal) cats ("Ihre Katzen sind."), it'll always be "sind". "Deine" is singular, "Ihre" is plural.
So, "sind" is solely determined by the count of the subject. If it was a single cat, "sind" would become "is": "Cat is." - "Deine Katze ist willkommen." - "Ihre Katze ist willkommen."
The noun, gender and case the noun is used in determine whether to use
deine in front of it.
dein is used with masculine and neuter nouns.
Mann is masculine,
Schwein (pig) is neuter. You can say
Dein Mann ist willkommen. or
Dein Schwein ist willkommen.
Deine, on the other hand, is used with feminine nouns and nouns of any gender in plural.
Frau is feminine. So the sentence would read:
Deine Frau ist willkommen. But, using the above nouns in plural you would also use
Deine Männer sind willkommen and
Deine Schweine sind willkommen.
The above rule is for nouns in nominative case only. In this sample sentence the noun is the subject of the sentence and the subject is always in nominative.
But: there are more word endings (these are called declensions, by the way). For instance, in
Ich sehe deinen Mann (I see your man/husband), Mann is the object of the sentence in accusative, hence the
en ending in
Ich sehe dein Schwein you notice that
dein has the same ending as in nominative above for neuter and masculine nouns. Here,
Schwein is in accusative though.
For feminine and plural nouns the ending happens to be the same as in nominative for them too:
Ich sehe deine Frau. and
Ich sehe deine Schweine.
possessive pronouns are inflected, just like adjectives. So there are different endings depending on number, case and gender of the qualified noun.
"dein" is the form for masculine singular nominative and neuter singular nominative or accusative, "deine" is feminine singular nominative and accusative as well as plural nominative and accusative.
See the full table here:
Depends on case, number and gender. Possessives are inflected.
different forms of the same word. "deine" can be nominative and accusative singular feminine as well as nominative and accusative plural (here it is nominative plural), "dein" is nominative singular masculinum as well as nominative and accusative singular neuter.
Whether the sentence makes more sense or not in a modified version is irrelevant. The sentence stands and is to be translated for exercise.
Your modification changes the meaning of the sentence significantly.
Your cats are welcoming. is quite different from
Your cats are welcome.
And, of course,
Your cats are welcome. is a perfectly fine sentence.
Perhaps adding the following will make it clearer to you what is meant by it:
Your cats are welcome in my house.
This sentence is quite the false friend as the straight translation of
sind willkommen has a transposed meaning in English, as
you're welcome is predominantly a response to
thank you. This is not what is meant in this sentence though.
To disambiguate this meaning in the English translation is difficult, if not impossible to achieve without context and will confuse a lot of native speakers of English.
I agree that the sentence is an ill-advised choice in a beginner lecture, but one could also argue that it makes the student think more.