Control was not easy - this gives an extra spin to Frontinus' idea of mathematization as imposing order on a territory. The imposition of order is a dialectic, dynamic process through which a model of administrative control is applied to the specific nature of a place. This dynamic implies a negotiation of various factors, and I think that the role played by mathematics and by mathematical imagery in this negotiation is fundamental.
...mathematics guaranteed the possibility and reliability of calculations, and made cataloguing and recording easier, so it was ‘directly’ useful.
Finally, Frontinus chose one particular type of pipe, the quinaria, as the standard type and ruled that authorized standard pipes and nozzles had to be stamped with an official mark, and no unstamped pipes or nozzles could be used.
Imposing a standard is clearly at the same time a pragmatic administrative choice - uniformity facilitates repairs and control of misappropriations - and a political one - the fact itself that someone has the authority to set a standard unequivocally signals where the power lies.
-- Cuomo, Serafina (2000). Divide and rule: Frontinus and Roman land-surveying. Studies in History and Philosophy of Science Part A 31 (2)189-202.
Using "free-monoidable" structures enables a radical simplification of control procedures ("arrows"). The first example has to do with making land "monoidable" through mathematized surveying. The second example shows how standardization of elements enables administration of infrastructure and distribution of resources.