When it comes to categories that are powerful or influential, there are a variety of synonyms to choose from. Examples include robust, well-established, dominant, leading, dominant, dominant and heavyweight. Other options might include unassailable, formidable, stalwart, indomitable and potent. The term 'powerful' is another common synonym for 'strong category', as is 'influential'. In some cases, words with a more specific meaning might be a better fit. For instance, if you want to emphasize the breadth of a category's influence, terms like 'diverse' or 'comprehensive' might work well. Ultimately, the choice of synonyms will depend on the context and specific connotations you're looking to convey.