Hey Tmize,
Thank you for reaching out!
The Events Calendar does allow for a basic “Category archive” page, so that if you click on an Event Category, you are brought to a filtered version of the calendar views which only shows events in that specific category.
A good example of this is on our demo site here, for the “Tech Meetups” category → http://wpshindig.com/events/category/tech-meetups/
Now, you’ll notice that the calendar views are the same as they are if you weren’tfiltering by a specific category…but only events in the selected category are on these category archive pages. And yes, they are in date order.
I hope this is making sense, and is helpful—let me know!
If you have your own specific page template that you want specific categories to show up on, then unfortunately no, there is not a way to events in that specific category on that template unless you write custom code.
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The Events Calendar is totally free, and these category-specific features are fully included in the free plugin, so the best bet here in my opinion would be to just download the plugin and set up on maybe a test site or a local development site or something—tinker around with it and see how it integrates with your goals. It might be exactly what you’re looking for!
Cheers,
George