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When you open a podcast, it shows numerous categories that are not listed in the drop down menus when searching for new podcasts or under the trending podcasts list (history is one that comes to mind). These should also be searchable. . Using "history" as am example, if the podcast doesn't have that word in it, you don't get all podcasts that deal with history.
The app allows you to search every standard category. Some podcast user create their own category, but it’s not possible to display them all in the drop down menu otherwise it will have more than 20K entries ;)
Every podcast available on iTunes uses standard categories, so it shouldn’t be an issue