I made a big update to the wiki. I added an analysis of what is hopefully a consistent and complete conceptual framework for what operators are that explains why the categories are what they are and gives clear distinctions between each category.
There are also 7 (hopefully) fundamental categories identified.
The quick version is that there are list and non-list operators, both types can have operators that filter, transform or replace the inputs.
Then construction operators make the 7th category.
There can be operators that fit into more than one category, but those operators are equivalent to a sequence of operators that all fit into only one of the 7 categories.
Note: there are actually 8 categories, but non-list construction operators are never useful, so we ignore them.