Make category dropdown select available in frontend post creation form

I'd like to use MB to let users create posts on the frontend.
The issue seems simple, but I couldn't find a solution yet.
The user creating a post should be required to pick a category for his post.

How do I make a dropdown select field available that's filled with my existing categories?
I mean I know how to add a dropdown custom field, but how do get my existing categories listed as choices? And of course the form submission should assign the post to the chosen category.