 This is neat answer. The question is what status it has vis-à-vis the Problem of Style. Are morphism-styles merely a subgroup of styles or are they privileged? The former is uncontentious. However, the emphasis many structuralists place on structure preserving mappings suggests that they do not regard morphisms as merely one way among others to represent something. What they seem to have in mind is the stronger claim that a representation must be of that sort, or that morphism-styles are the only acceptable styles.