A long time ago I studied mathematics at the University of Stockholm. I had a romantic view of modern algebra and manage to make the first two algebra courses by self studies in order to immediately study homological algebra, Galois theory and such topics. That is not the best way to study. Later as a graduate student I did rather well - until the gaps in my basic knowledge and abilities began to affect too much. Then I stopped focusing on mathematics about 35 years ago.
I did self studies in category theory because we were supposed to do that and because it was a good idea. Category theory worked fine with the mathematics evolved at 1950 or so. The universal definitions and duality simplified a lot of mathematics as tensor products and injective/projective modules etc and the functors opened new possibilities.
The last 40 years or so the interest in and the development of category theory has exploded and seems nowaday be very abstract but also very consistent.
My question is, what modern category theory could be interesting for a person mainly interested in the mathematics concerning structured sets?
The bounty will soon expire and there is 50+ in reputation to earn - aren't there anything to express on this topic?