BEATING THE POISONED DRUM

Master Tosotsu Etsu conceived a triad of conundrums for his students:

1. Ponder the odyssey of a seeker (S) navigating the complex constellation of existence, represented as a category (𝔼), wherein the objects symbolize distinct states of being, and the morphisms epitomize the intricate web of transformative experiences. Guided by the sagacious insights of an enlightened master (M), the seeker endeavors to unveil the enshrouded architecture (𝕳) that governs their inner truth (T) through a geometrically-defined manifold (𝔾) and a functional programming paradigm (𝔽). As esteemed adepts in the esoteric discipline of categorical algebra, geometry, and programming languages pertaining to the soul’s mysteries, at the present vertex (t₀) within the multidimensional fabric of spacetime, can you ascertain the unique initial object (𝟘) and terminal object (𝟙) in the category (𝔼) that demarcate the pivotal nexus (P) where your quintessential nature (N) converges with the cryptic equation underpinning the universal path to enlightenment?
2. Upon unearthing the essence of your intrinsic nature (N), you disentangle the enigmatic theorem of transcendence (Φ) by constructing a geometric representation of self-awareness within the context of a programming language, which encapsulates a natural transformation between a pair of functors – one signifying the cyclical duality of life (L) and death (D), and the other embodying the elusive sphere of liberation (R). As the radiance of your perceptual faculties (F) inexorably gravitates towards the threshold of dissolution (δ), how will you synthesize the isomorphism (ι) that equates your quintessence with the harmonious expanse of unbounded emancipation (R), transcending the limitations imposed by the ephemeral nature of corporeal existence?
3. Having attained the sanctum of liberation (R) from the intricate cycle of life and death (L, D), you are endowed with the hallowed knowledge (K) of your preordained destination (D’), which resides in an exclusive category of celestial sanctuaries (𝔸). In anticipation of the eventuality where the four elemental cornerstones (E₁, E₂, E₃, E₄) constituting your existence disintegrate into their primordial constituents, what is the adjunction (𝔸 ⊣ 𝔼) between the categories of 𝔼 and 𝔸 that delineates the precise functor (F) responsible for transmuting your essence from the realm of circumscribed experiences to the infinite dominion of cosmic harmony (C)? Furthermore, can you devise an algorithmic procedure, leveraging the power of a geometrically-informed programming language, to facilitate the seamless metamorphosis of your being into the boundless ether of the cosmos?