” there must be no definitional contradictions inbuilt into the subconcepts being linked by your categorizations.” would be a significant part of your theory of the category of categories.
Turtles all the way down but it’s functional.
You’ll notice we have a distinction of priority in our modelings.
I prioritize pragmatism. You prioritize non-contradiction. Your modeling includes pragmatism as mine includes non-contradiction (implied by its “needs at the time” usage) but our priorities differ.
For example, up until the point of the “doing” (the event), contradiction can be a part of the potential of a system.
My computer circuit could allow the collision of contradictory values and hang up for example even if it’s outside of specifications.