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No, I didn't unpublish the sermons at all! You can also see in the category view that there are 3 sermons in it. You can see on the (quite bad quality) screenshots my backend, they are all published. If it's something with the SQL, what can I do? Remove the whole component and install it from scratch? (I have already reinstalled the v4.4.4 at least 2 times, but nothing has changed)

mod: yes, meanwhile I've found the language files in the admin-folder

You use SermonSpeaker 4.4.4? Can you please install SermonSpeaker 4.4.5? SermonSpeaker 4.4.4 has a nasty bug.

You can try to enable the error reporting from Joomla and see if you get any errors. Also check the server error log if there are any errors there.

I tried to reproduce it on my testing server and here it works.

I have enabled now joomla error reporting, you can check it, probably you'll find some useful info. I see that it checks if the category is equal to 30.. but what do the other commands do?...
I upgraded now from 4.4.4 to 4.4.5, nothing changed.

mod: attached you can find the joomla SQL-log

There is also an error reporting in the server tab which you can set to "maximum". This would show any PHP errors.

If you have access to phpMyAdmin or a smilar tool, you can test the SQL statement from the debug info directly in the database and see if it gives you an error.
The statement in question would be the one on step 10 (or 11).

Did you install SermonSpeaker 4.4.4 directly as a fresh install? Or was it an upgrade from a previous version?

Now, PHPmyadmin was a good idea

It didn't work, because it filtered on the speaker_id too, and when I edited the speaker, I forget to set the category for it. Now I set it, and it works! Thanks

I'll send the hungarian translation if I manage to fully complete it..

But how is it that I can only set one Category for a Speaker? I have two categories (Sermons and Evangelisations), and I have a speaker who I want to set as speaker in sermons in both categories.