Variant or alternative form of hegemonic; relating to or characterized by the dominance of a hegemon.
Formed from 'hegemonic' plus the -al suffix, or independently from 'hegemon' with both -ic and -al suffixes. This is an older or more formal variant found in academic and philosophical writing.
The fact that we have both 'hegemonic' and 'hegemonical' shows how English sometimes creates variant adjective forms—usually the -ic version becomes standard over time, and the -ical version sounds more archaic or formal, like comparing 'historic' to 'historical.'
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