Another way of doing this is with Contextual filters
-Create a view display Page (Block also works)
-Add Contextual filter Content has Taxonomy Term ID
-Leave When the filter value is NOT in the URL as Display all results
-On When the filter value IS in the URL or a default is provided check 'Specify validation criteria' and choose the vocabulary that has your events categories, leave filter type as 'Term ID'
Now when you hit the page url example.com/events it will list all the events from all categories
When you hit example.com/events/1 it will only list events from the category that it's term ID is 1 (say family is id 1 and outdoors is id 2, it will show all events categorized as family)
You could also make it filter by more than one term with other configurations options, and create URL aliases so your url becomes example.com/events/family