No, it must be polyphonic
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At the related link below is an example of a modern fugue written by Nick Vasallo, a 21st century composer. It is also a tribute to J.S. Bach, the master of fugue.
well, technically it would just be unison, but it could also be called monophonic.
Gregorian Chant
Monophonic: Only one part or voice.Homophonic: More than one part or voice, but all moving at the same time.Polyphonic: More than one part or voice, all doing their own thing.