Hey Tomasz and thanks for getting in touch!
Yes, every category does get it’s own unique URL which can be linked to directly. For example, if I have an event category called Birthday, the URL would look something like:
[my-site]/events/category/birthday
Events Calendar PRO also includes a shortcode for embedding the Mini Calendar and List View widgets and both include the ability to filter those widgets by category as well.
Does this help answer your question? Please let me know. 🙂
Cheers!
Geoff