In the Azumanga Daioh universe, only Sakaki and Osaka seem to have the shared image of Chiyo-chichi as a yellow cat(-like creature), and he is visible to the viewer a few times. If we go by Carl Jung’s definition of the extravert and introvert, (as far as I remember) the introvert is more in touch with the collective unconscious and the archetypes while the extravert is more in touch with the persona and the outside world. Since two characters that are aware of Chiyo-chichi can be considered as introverts, could Chiyo-chichi be a part of the collective unconscious? That could also explain why there exists plushies in the image of Him in the Azumanga Daioh universe.
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I completely missed this post. I really know nothing about the “collective unconscious”. It’s anime so it is possible that they somehow just have a mystical connection with each other and share thoughts. I think they dream up Chiyo chichi because they have both seen the plushies. That doesn’t really explain why they both think of it as Chiyo’s dad though. Sasaki tells the gang on Chiyo’s birthday that the yellow cat is Chiyo’s father but I can’t remember if this was before or after Osaka dreams of him.