"under the general category" is correct and commonly used in written English.
It can be used to indicate that something is classified or grouped within a larger or more general category. Example: "Fruits and vegetables fall under the general category of healthy foods."
Within reason, the bride may ask her attendants to pay for their hair and makeup, which fall under the general category of wedding attire.
The proceeds from these credit cards fall under the general category of ancillary fee revenue, which these days make the difference between profit and loss on most domestic carriers.
Several mystery writers, including R. J. Ellory, Stephen Leather and John Locke, have recently confessed to various forms of manipulation under the general category of "sock puppets," or online identities used to deceive.
Corporate data fall under the general category of administrative data and provide varied information on the worker and workplace.
This analysis is based on machine learning and statistical techniques as well as other more recently developed techniques that fall under the general category of data mining.
This hyperadrenergic state, in combination with excess cytokine production, results in a spectrum of myocardial injury often grouped under the general category of septic cardiomyopathy.
Transposon-based insertional mutagenesis vectors used in zebrafish fall under the general categories of enhancer trap, 5' gene trap and 3' gene trap, and include fluorescent reporters to detect "trapping" events.
Within this list of newly opened venues, 32% of the venues fall within the general category of Food, 32% under Travel & Transport, and 8% under Nightlife Spots.
Isn't it enough to know the general shape, the general category?
"Obviously it is in the general category but slightly different".
As intended by the authors, they are mostly subsumed under the more general category of children.
