# Towards a (meta-)mathematical theory of consciousness: universal (mapping) properties of experience

arXiv: https://arxiv.org/abs/2412.12179 · HTML: https://mlsanity.com/paper/2412.12179/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [The Reflexive Integrated Information Unit: A Differentiable Primitive for Artificial Consciousness](https://mlsanity.com/paper/2506.13825/) (2025)

## Abstract (arXiv)

Conscious experience permeates our daily lives, yet general consensus on a theory of consciousness remains elusive. In the face of such difficulty, an alternative strategy is to address a more general (meta-level) version of the problem for insights into the original problem at hand. Category theory was developed for this purpose, i.e. as an axiomatic (meta-)mathematical theory for comparison of mathematical structures, and so affords a (formally) formal approach towards a theory of consciousness. In this way, category theory is used for comparison with Information Integration Theory (IIT) as a supposed axiomatic theory of consciousness, which says that every conscious state involves six axiomatic properties: the IIT axioms for consciousness. All six axioms are shown to follow from the categorical notion of a universal mapping property: a unique-existence condition for all instances in the domain of interest. Accordingly, this categorical approach affords a formal basis for further development of a (meta-)mathematical theory of consciousness, whence the slogan, ``Consciousness is a universal property.''