The monoid-now: a category theoretic approach to the structure of phenomenological time-consciousness.

Human consciousness is characterized by constant transitions in time. On the other hand, what is consciously experienced always possesses the temporal feature of "now." In consciousness, "now" constantly holds different contents, yet it remains "now" no matter how far it goes. This duality is thematized in Husserlian phenomenology as "the standing-streaming now." Although this phrase appears contradictory in everyday language, it has a structure that can be clearly understood and formalized. In this paper, we show that this structure can be described as a monoid in category theory. Furthermore, monoids can be transformed into the coslice category, which corresponds to the way of perceiving present moments as juxtaposed in succession. The seemingly contradictory nature of the "now" as both flowing and standing can be precisely structured and comprehended through the monoid, while the perspective of the "now" as discrete points on a timeline can be effectively formalized using the coslice category. This framework helps us more precisely understand the differences between ordinary consciousness and meditative consciousness, specifically the experience of the "eternal now." We illustrate how the meditative states of consciousness presented in the early Buddhist scriptures (Pali Canon) and Dōgen's