Consciousness in a Higher Categorical Context
Renaud Gauthier
TL;DR
This work develops a higher-categorical framework for consciousness within a Segal topos by pairing a fluid, micro-reversibility driven δ-formalism with a consciousness-based $\mathbb{K}$-formalism. The δ-formalism constructs a long directed system of thickened neighborhoods $\text{d}\mathds{1}[p\epsilon]$ whose colimit recovers the ambient ground state $\Omega$, thereby giving a point-independent presentation of $\text{d}\mathds{1}$. The $\mathbb{K}$-formalism uses the Grothendieck construction to organize evolving consciousness towers over thick points into categories cofibered in groupoids, yielding a dual yet compatible representation $\mathbb{K}$ of the same phenomena. A global–local duality is established between the passive δ-driven immersion and the active, consciousness-generated $\mathbb{K}$-decomposition, which together reconstitute the ground state $\Omega$ from the reconstructed base $\mathds{1}$. The results suggest a formal roadmap for reconciling determinism and free will within a unified higher-categorical description of natural phenomena and consciousness.
Abstract
We provide two representations of the Segal category $\mathcal{X}$ modeling natural phenomena, the first one being based on the concept of micro-reversibility, producing a long sequence $Σ$ of categories as a resolution of $\mathcal{X}$, the second one providing graded categories cofibered in groupoids over the categories of $Σ$, using the concept of consciousness as impetus. We show those two representations are dual to each other.