Grouping, Aggregate, Min, Max

I am not sure how to define with words what I want to accomplish (so can't ask google the right question :) )

So will try to explain with sample data and expected result:

Scenario 1)

Expected result:

(Sounds easy, group by, thing_id, category use Min and Max for period id - but further scenarios makes it a bit complicated...)

Scenario 2)

Expected result:

Scenario 3)

Expected result:

So goal is, to group by thing_id, category id - but if period_id is interupted (not in incremented by 1) to have aggregated spans...

To desired results we have came up using several CTE's (what makes a query a bit big, and more "procedural way": make cte what calculated diff between current and previous row, next cte uses previous one to define groupings, next cte to make aggregates etc...)

So I wonder - is there some kind of aggregate window function what does desired results?

Many Thanks,

Misa