> It has often led to problems and complicated equations being represented with far more simplicity.
How? AFAICT, the string diagram contains far too much incidental information for doing linear algebra. It contains even more information that a fully parenthesized tree of additions because it even contains information about how to evaluate duplicated expressions (eg. it tells if in (x+y)+(x+y) you should evaluate (x+y) twice or only once and then reuse the value). If we write a string diagram as a normal linear system the whole question of fullness and faithfulness would be dead obvious.
How? AFAICT, the string diagram contains far too much incidental information for doing linear algebra. It contains even more information that a fully parenthesized tree of additions because it even contains information about how to evaluate duplicated expressions (eg. it tells if in (x+y)+(x+y) you should evaluate (x+y) twice or only once and then reuse the value). If we write a string diagram as a normal linear system the whole question of fullness and faithfulness would be dead obvious.