# A Category Theory Account of AI Identity

arXiv: https://arxiv.org/abs/2607.00220 · HTML: https://mlsanity.com/paper/2607.00220/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [Machine Learning Operations (MLOps): Overview, Definition, and Architecture](https://mlsanity.com/paper/2205.02302/) (2022)
- [Towards a Science of AI Agent Reliability](https://mlsanity.com/paper/2602.16666/) (2026)
- [A Trustworthiness-based Metaphysics of Artificial Intelligence Systems](https://mlsanity.com/paper/2506.03233/) (2025)
- [A Multivocal Review of MLOps Practices, Challenges and Open Issues](https://mlsanity.com/paper/2406.09737/) (2024)
- [High-Risk AI Systems and the Problem of Identity in the European AI Act](https://mlsanity.com/paper/2605.23922/) (2026)
- [Update Opacity: Epistemic Accessibility and Governance Under AI System Change](https://mlsanity.com/paper/2606.00037/) (2026)

## Built on by (most cited first, 2 of 2)

- [Operational Identity: A Finite Audit of Declared and Implemented Rules of Sameness](https://mlsanity.com/paper/2607.20729/) (2026)
- [Convex AI Compositionality and the Governance of AI System Populations](https://mlsanity.com/paper/2609.24784/) (2026)

## Abstract (arXiv)

Artificial intelligence (AI) systems are routinely modified after deployment through retraining and changes in their environments. These transformations raise a metaphysical question: under what conditions does an AI system remain the same system over time or across deployments? Earlier work formulates synchronic and diachronic identity propositionally, by relating identity within a fixed AI system type to equality of trustworthiness levels. Such criteria specify when identity statements are true, but leave implicit the structure of the states compared, the transformations connecting them, and the temporal organization of persistence. We develop a category-theoretic formalization of AI identity. An AI system type is specified by a datum consisting of a techno-function, a trustworthiness profile, and a trustworthiness-level function. Profile-relative states are connected by admissible lifecycle paths, which are restricted to trustworthiness-level-preserving transformations and quotiented to obtain a reachability category. Temporally admissible functors represent AI system histories, while time-synchronous natural transformations compare realized histories. The formalization yields two categorical interpretations of the earlier AI identity criteria. A weak interpretation recovers identity as equality of trustworthiness level. A strong interpretation requires mutual trustworthiness-preserving reachability, expressed through state isomorphism or natural isomorphism of realized histories. Category theory therefore replaces a single AI identity relation with a structured hierarchy of diachronic and synchronic criteria. The resulting framework identifies identity-related preconditions for transferring responsible-AI claims, evidence, and governance procedures across versions or deployments, without treating categorical identity as sufficient by itself for such transfer.