We have 6 different libraries. All of them are working with a checkbox column (management). Is it possible to run a script or something like that, which grabs all documents (management = yes) and copy those into another library? Or show them in one list to open it with the explorer view?
Your best bet would be using Event Receivers. That, though, requires developing a custom component. Here is a simple HOW-TO
What you need is an ItemAdded event receiver, which would check the value of Management column and if it's true, the document would be copied to a different library. You can handle ItemUpdated event as well, if someone decides to change Management No to Management Yes.
Other way to do it would be a Ribbon button which would open up an application page. On that page you can use a caml query to get items from all your 6 libraries or use an SPSiteDataQuery if the number of libraries might change in the future. Examples Here and Here
Hope this helps.
@paul-strupeikis has the correct answer here IMHO, but I would like to point out a straight forward alternative (albeit not as pretty):
Consider using PowerShell in a Scheduled Task.
It depends on how instant you need the transferring to occur, but if you could let it wait 2-5 minutes then this approach could be a good enough solution for you.
We find ourselves using this approach often, as I find it easier to get an overview of all the "batch jobs", and it's easier to maintain/change (can be a bad thing).
See this gist for a starter template.