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Categorical Longevity: Category Theory & Computational Biology Well-being

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Melanie Swan at DIYgenomics
Melanie Swan
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Takashi Kido
Takashi Kido
Takashi Kido
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Renato P. Dos Santos at Lutheran University of Brazil
Renato P. Dos Santos
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Abstract

Categorical Longevity is introduced as a computational systems biology approach which applies category theory to unify and formalize the activity, metrics, and interventions of biological systems in addressing the accelerated multisystem decline characteristic of human aging. By providing a comprehensive and computation-ready framework, this method integrates diverse mathematical models and data representations, enabling a deeper understanding of biological dynamics across scales. While advancements such as hallmarks of aging , biomarkers, epigenetic clocks, and organ-specific aging metrics have proliferated, the absence of a standardized framework limits their joint analysis and practical application. Categorical Longevity addresses this gap, offering tools for multiscalar analysis, robust dynamical modeling, and the integration of computational technologies such as blockchain to facilitate scalable, secure population-level deployment. Category Theory and Longevity A modern scientific trend is formalization, meaning the extensive use of mathematical models, algorithmic analysis, and computational instantiation. This is seen in deep learning as a foundational technology used in many fields, with the concept technology connoting active processes involving compute, algorithms, and data. Category theory (Eilen-berg and MacLane 1945) provides a universal language for formalizing the modeling of physical, chemical, and biological systems in a computation-amenable way (Spivak 2014). In biology, for example, categorical genomics attempts to organize vast data volumes into a coherent whole. One project identifies Dist (distance) as a category for genes, a structure unifying the descriptive gene-related sub-categories of open Petri nets (gene regulatory networks), preorder (gene orders), operad (gene trees), and olog (gene ontology) (Wu 2023). Another project specifies a genetic algebra with the categories Set and Semimodules to study genotype, phenotype , and haplotype groups (Tuyeras 2018). Longevity entails potentially curing the diseases of aging. Aging is the primary driver of many leading causes of death,
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Categorical Longevity: Category Theory & Computational Biology Well-being
Melanie Swan1, Takashi Kido2, Renato P. dos Santos3
1University College London
2Teikyo University
3academicum.ai
melanie@DIYgenomics.org, kido.takashi@gmail.com, info@academicum.ai
Abstract
Categorical Longevity is introduced as a computational sys-
tems biology approach which applies category theory to unify
and formalize the activity, metrics, and interventions of bio-
logical systems in addressing the accelerated multisystem de-
cline characteristic of human aging. By providing a compre-
hensive and computation-ready framework, this method inte-
grates diverse mathematical models and data representations,
enabling a deeper understanding of biological dynamics
across scales. While advancements such as hallmarks of ag-
ing, biomarkers, epigenetic clocks, and organ-specific aging
metrics have proliferated, the absence of a standardized
framework limits their joint analysis and practical applica-
tion. Categorical Longevity addresses this gap, offering tools
for multiscalar analysis, robust dynamical modeling, and the
integration of computational technologies such as blockchain
to facilitate scalable, secure population-level deployment.
Category Theory and Longevity
A modern scientific trend is formalization, meaning the ex-
tensive use of mathematical models, algorithmic analysis,
and computational instantiation. This is seen in deep learn-
ing as a foundational technology used in many fields, with
the concept technology connoting active processes involv-
ing compute, algorithms, and data. Category theory (Eilen-
berg and MacLane 1945) provides a universal language for
formalizing the modeling of physical, chemical, and biolog-
ical systems in a computation-amenable way (Spivak 2014).
In biology, for example, categorical genomics attempts to
organize vast data volumes into a coherent whole. One pro-
ject identifies Dist (distance) as a category for genes, a struc-
ture unifying the descriptive gene-related sub-categories of
open Petri nets (gene regulatory networks), preorder (gene
orders), operad (gene trees), and olog (gene ontology) (Wu
2023). Another project specifies a genetic algebra with the
categories Set and Semimodules to study genotype, pheno-
type, and haplotype groups (Tuyeras 2018).
Longevity entails potentially curing the diseases of aging.
Aging is the primary driver of many leading causes of death,
Copyright © 2025, Association for the Advancement of Artificial Intelli-
gence (www.aaai.org). All rights reserved.
including type 2 diabetes, neurodegenerative disease, and
cardiovascular disease, as organisms experience accelerated
decline (entropy) with aging (Cipriano et al. 2024). In recent
years, quantization has been a primary trend in longevity.
This has been through the identification and validation of
biomarkers (Lyu et al. 2024), hallmarks (Lopez-Otin et al.
2024), data collection methods (Mengelkoch et al. 2024),
and intervention (Guarente et al. 2024). The implication of
measurement is having quantitative metrics for targeted in-
tervention. However, these quantitative measures have not
been assembled into an overarching formal structure.
Hence, Categorical Longevity is introduced as a research
program to consolidate the quantitative systems biology of
aging into a standardized approach. Implementation could
be by composing a category Longev (in the vein of Dynam,
a dynamical open system category (Baez and Pollard,
2020)), with four sub-categories for hallmarks, biomarkers,
data, and interventions. Each category has category objects
(e.g. the twelve hallmarks of aging), morphisms (mappings)
between them (e.g. DNA mutation and damage repair rates),
and functors (equations relating categories).
Categorical Longevity may be deployed at three levels.
First is in the use of category theory in mathematical models
used to describe underlying biology directly (e.g. Petri nets
representing epigenetic change (Bardini et al. 2016)). Sec-
ond is in category-theoretic approaches to the mathematical
analysis of biological data (e.g. topological data analysis of
cancer tumors with persistent homology (Stolz et al. 2024)).
Third is via category-theoretic approaches used in AI ma-
chine learning applications in biology such as drug design
(e.g. monad algebras in a 2-category of parametric maps in
categorical deep learning (Gavranovic et al. 2024)).
Categorical Longevity Toolkit
Category theory operates at the level of mathematical struc-
ture shared across objects, abstracting away from the detail
of content. The broader argument of Categorical Longevity
is the use of category theory as a toolkit for diagnosing the
kinds of formal problems at hand and analyzing them in an
overarching framework that connects to other problems. A
unified formal framework could be indispensable in ad-
dressing the complex systems biology of aging. Some of the
kinds of formal problems are dynamics, multiscalarity, con-
currency in distributed systems, and optimization.
Dynamics: Rate Laws
A broad trend in biological study is dynamics. A challenge
is that traditional models (e.g. Lotka-Volterra predator-prey)
have only basic dynamics. Hence, more sophisticated mod-
els are needed such as entropy-based measures that build to
an “effective temperature” of aging (Denisov et al. 2024).
Petri nets are a categorical method used to model biochem-
ical processes in which tokens accumulate at network nodes
to trigger an event. More robust dynamics could help (e.g.
to model DNA damage signaling (Gutowska et al. 2022)).
Multiscalarity: Duality
Multiscalar systems have different mathematics at different
scale tiers, as captured in the integrated analysis of hybrid
PET/MRI brain scans (Munn et al. 2024). The category-the-
oretic concept of duality allows one scale to be viewed from
another. For example, the Heisenberg and Schrödinger pic-
tures of quantum mechanics are brought into a unified pic-
ture with AQFT-FQFT (algebraic and functorial QFT)
(Schreiber 2008), applying to neural field theories of aging.
Research Agenda
Categorical Longevity research projects could include:
• Algebraic topology analysis of genome TADs (topologi-
cally associated domains) in metabolic pathways
• Enzyme kinetics (Michaelis-Menten) applied to Petri net
model of DNA mutation and damage repair rates
• Knot theory hypergraph model of senescent cell clearance
• 2-Segal space simplicial sets for immune system analysis
• AQFT-FQFT field theory of aging per amplitude metric
• Feynman category fibration-foliation duality analysis of
accumulated damage of aging and inflammation profiles
Conclusion
Categorical Longevity is introduced as a research program
for the interconnected formal analysis of the systems biol-
ogy of aging. Category theory is growing in use in the com-
putational infrastructure (e.g. in smart network technologies
deep learning (endofunctor algebras), quantum computing
(categorical quantum circuits), and blockchain (categorical
cryptoeconomics)), readily extending to computational biol-
ogy. Blockchain is implicated for the implementation of
Categorical Longevity, practically due to its secure compu-
tational substrate, and theoretically due to its tokenized na-
ture facilitating the energy-entropy bookkeeping of longev-
ity solutions with causal histories in digital health twins.
Overall, Categorical Longevity provides a comprehensive
formal approach for global well-being that addresses both
the worldwide demographic shift in aging populations as
well as the on-boarding of new computing platforms such as
BCIs (brain-computer interfaces).
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