"Once category theory was developed and used, in particular when the central theoretical role played by adjoint functors was understood, a fascinating process of reversal of perspective, a gestalt switch, took place: what was seem as a useful tool in organizing and guiding mathematical thought became a theoretical framework that revealed the basic or fundamental principles underlying mathematical concepts, theories and theorems. Thus, the Stone duality theorem is indeed more perspicuously presented in the context of categories and functors—it is organized nearly and the basic consequences of the result are transparent—but once it is seen as a special case of a very general adjoint situation, a theoretical understanding of the phenomenon becomes available. Category theory is not applied to Stone's theorem, it is the latter that becomes a specific instance of a general, universal conceptual situation.
Although it might in the end be more obscure than what I have said so far, I dare at this stage put forward a slogan that, I believe, sums up the core of what I have been presenting: category theory is the architectonic of mathematics. Category theory is, indeed, as in the philosophical sense of the expression "architectonic", the systematization of mathematical knowledge. Mathematical knowledge is systematic. Mathematics is a conceptual system. That much is indubitable."
Note that it's -tectonic (from the Greek for carpenter) not -ectronic (from electron). And it's just "the architectonic of mathematics", not concepts in general. There are obviously architectonics of other things as well, like (spatial) architecture itself, or music, or cooking. So while perhaps CT is the ultimate theory of algebraic abstractions, but it's not the only kind of design system that exists. It represents the mathematical aspect of design.