Thanks for mentioning the difficulty-wise split. Somehow slipped my mind while I was writing the blog, but I think it's a very important feature to have.

In my opinion, the redundancy issue is not just limited to viewing the catalog. When someone adds a blog to a category, they implicitly assume that there is meant to be a single category per blog (and moving previously added blogs to multiple categories takes a lot of operations). I think an explicit mention of the possibility of multiple tags will make it much better.

I would not put the difficulty as a top level distinction; rather, I would add a 3-star or 5-star difficulty rating to every problem and agree to generally order blogs within a category by the difficulty.

In that specific case, me neither. It really just talks about permutations, and it should have a single tag that signifies that. My main concern in this specific case was the fact that if there is still no consensus on such simple blogs, maybe there is something wrong with the categorization as it is now. Hence the part that says "I wonder how to categorize blogs that take a topic and try to collect some ideas around that topic. General idea based blogs are currently categorized under a general section under algorithms, and they suffer from the same issue, but to a lesser extent because they are kind of global."

In the remaining cases, I think the concern is genuine, and the blogs really talk about more than one thing. For example, the blog on segment tree talks about how to do certain kinds of optimizations in C++ (not limited to segment trees), and including it in the section on segment tree only is a bit weird. Similarly, the Mobius inversion blog is more of a general idea in algebraic combinatorics, than just a generalization of something you see in NT (maybe it would make sense to remove it from NT and add it into some other specific category). And it is surprising that the blog on visualizing geometry is not in tools.