We don't formally present the Category ID in the UI in an easy to retrieve way, but there are a couple of technical ways to get to that ID:
Option 1: Inspecting the HTML of the "Manage Categories" Popup
If you open the "Manage Categories" and inspect the HTML for the "edit" link, you will see an HTML property labeled "data-id"
Here we can see that the Category ID for "FAQ" is 1001
Option 2: Using Jive's v3 API system
There is an API end point for specifically getting a list of categories that belong to a place. The documentation is here: https://developers.jivesoftware.com/api/v3/cloud/rest/PlaceService.html#getPlaceCategory(String, String, String)
Here we can run an API call like the following for a place:
Here we can see a category called "FAQ" with an ID of 1001
Option 3: Querying a copy of the application database
If you have access to a copy of the Jive application database, you can also query the tables to find the unique IDs for each category. The category records, and their IDs, are in the jivetagset table.