Category theory is a widely applied diagram-oriented mathematical theory of algebra. Generally, mathematical science diagrams use arrows, labeled with symbols, to connect between other symbols. Each type of diagram has its own formation rules, its “syntax”. Some types have transformation rules, and sequences of transformed diagrams form a “cartoon strip” of two-dimensional calculation and reasoning. Euclidean Geometry and Category theory diagrams are like that. But, in category theory there is also a one-to-one correspondence between diagrams and systems of algebraic equations, so that its two-dimensional calculations correspond exactly to algebraic calculations with one-dimensional expressions. The combination of such diagrams and their equations is a most elegant notational tool for…
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