"Do you have a workout on Monday?"
Translation:У вас є тренування у понеділок?
Would "У вас тренування у понеділок?" work here? Someone mentioned something similar in an earlier question, I believe it was "У мене тренування уранці"
Yes, you can skip it in this case.
In general "У мене/тебе/нас/... є" means "I/you/we/... have", so you can't really say "У мене кіт" instead of "У мене є кіт" (unless it's a clever joke in some context), but in this case you can say it. "У мене тренування в понеділок", "У мене завтра робота".
It didn't accept it when I tried it, so I'll report it next time this question comes up. Thank you!
What does the initial "У" do in the phrase "У мене/тебе/нас/... є..."? Without it, would the sentence not still read "To me/you/us... there is..."?
Is it needed because we are using accusative pronouns instead of dative pronouns?
It doesn't have a direct equivalent in English. It serves the functions of in and at.
E.g. "у ванні" = in the bathroom, "у школі" = at school.
Also, since I see you're doing German as well: "у мене" is similar to the German bei mir. It can be used the same way, e.g. to mean "my place" or "your place": "Wo spielen wir heute, bei mir oder bei dir?" = "Де ми граємо сьогодні, у мене чи у тебе?"
So, literally, "У мене є кіт" = "Bei mir ist eine Katze" or "Bei mir gibt es eine Katze"
Thank you, that is very helpful.
I just want to point out to anyone in the audience, to avoid confusion, that while the German language uses the dative case for this phrase ("mir" instead of "mich"), the Ukrainian language uses the accusative case ("мене" instead of "мені").
This is true!
One way to say you have/own something is also "Мені належить" (belongs to me) which is like "Mir gehört" and the cases "match".
But this "мене" is also a bit special... The actual Accusative of "я" is "менé" with the stress on the last "е", while "у мéне" has the first "е" stressed. Same with "тебé" <-> "у тéбе". Same happens with "на", "до" and so on: "на/до/від мéне" ("auf mich"). I don't know what's happening there, but it's a thing :)