Ash began his journey with a Pikachu, inspiring Pokémon Yellow's creation, as well as causing some to consider Red and Ash to be the same person, most especially due to Red owning one as well.
As said there Red and Ash are counterparts. Ash won't evolve his Pikachu because he doesn't want to evolve. Making it possible that Red's Pikachu feels also the same way.
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