How do I link to a Media Library category?

You can create links to specific Media Library categories by appending /?c= and the specific category to the URL. For example, the Media Library at https://www.presspage.com/news/media-library has a category called 'Infographics', so the direct link would be https://www.presspage.com/news/media-library/?c=infographics.

Something similar can be done with tagged assets in the media library. The URL would look like this: https://www.presspage.com/news/media-library/?t=example.
Pay attention to the t (of tag) in the URL instead of the 'c'. 

You can link to multiple tags or categories simultaneously by separating them with a plus, like so: https://www.presspage.com/news/media-library/?t=example+example2.

Finally, you can create a direct link to the video tab in the Media Library by appending ?tab=video to the URL.