Form
The organization or pattern that can be recognized across different realizations.
THE FUNCTORISM PROJECTAN EVOLVING RESEARCH ATLAS
From representation
to intelligence.
How do systems represent their world, turn knowledge into action, and learn from what happens next?
A research program connecting category theory, cognitive architecture, and human–AI symbiosis.
Explore the foundations ↓THE CENTRAL IDEA 01 / REPRESENTATION
WWorld
F⟶representation
RRepresentation
F : World → Representation
A system encounters the world through representations. Learning changes how those representations guide action.
Developed by Dr. Richard Tong · 佟佳睿Foundations → Architecture → Applications
01 / FOUNDATIONSA vocabulary for intelligent systems
Begin with relations.
Follow the transformations.
Functorism proposes a common language for how physical systems carry information, construct representations, and become capable of adaptive action. These are working conceptual definitions within the research program.
Substrate
The physical medium in which a pattern is instantiated and transformations occur.
System
Interacting components whose relationships sustain an identifiable organization.
Information
A difference interpreted through a relationship between a system and what it represents.
Agent
A system that uses representations to guide action in relation to tasks or goals.
The mathematical lens +
A proposed categorical description writes F : World → Representation. To make this a genuine functor, a model must specify both categories, their objects and morphisms, and show that identities and composition are preserved.
F(idX) = idF(X) · F(g ∘ f) = F(g) ∘ F(f)
The mapping is a research commitment to formalize—not, by itself, a proof that every cognitive process is functorial.
02 / THE KSTAR LEARNING LOOPKnowledge becomes actionable
Predict. Act. Compare.
Learn.
Knowledge is more than stored content. In KSTAR, it generates an action plan and an expected result. Experience supplies the comparison that can improve the next decision.
(K, S, T)→(Â, R̂)→(A, R)→K′
S + T / ESTABLISH THE CONTEXTWhat is happening?
What is happening?
What are we trying to achieve?
The situation captures relevant context and constraints. The task identifies the goal and the criteria for a useful result.
ILLUSTRATIVE EXAMPLE · OPPORTUNITY ASSESSMENT
A team receives a potential customer project. It gathers requirements, available expertise, delivery constraints, and the evidence needed for a go/no-go recommendation.
K = skills + ontology + connectors + KSTAR memory. The loop distinguishes a planned action  from an executed action A, and an expected result R̂ from an observed result R.
03 / CONNECTED FRAMEWORKSOne research program, several levels
From a theory of knowing
to systems that learn.
Each framework addresses a different part of the same question: how can intelligence become grounded, persistent, collaborative, and capable of improvement?
Functorism
Relations among world, representation, and transformation provide the conceptual foundation for the wider research program.
F : W → R
A proposed formal language for representationKSTAR
Connects situation and task to forecast, action, observed results, and knowledge updates.
NEOLAF
Explores neural and symbolic memory, complementary computation, and agents that improve through experience.
Human–AI symbiosis
Studies how people and companion agents can coordinate, share context, and develop capabilities together.
04 / RESEARCH DIRECTIONSQuestions that drive the work
Intelligence is a beginning.
What follows?
01PHILOSOPHY & COGNITIONIntelligence, consciousness, and self-representation
+
Intelligence, consciousness, and self-representation
How should we distinguish successful problem solving from recursive self-representation, autonomy, and subjective experience?
This direction investigates possible dimensions of intelligent systems without assuming that benchmark performance or a self-model establishes consciousness. The relationship between functional organization and experience remains an open question.
02DECISION CAPABILITY & AUTHORITYThe meta-decision problem
+
The meta-decision problem
When can an AI make a decision—and when should it have the authority to do so?
The proposed Functorism–KSTAR approach distinguishes situated context, applicable knowledge, action plans with forecasts, and authority or access. It treats demonstrated capability and delegated decision rights as separate requirements.
03AGENT SYSTEMS & ENTERPRISE COGNITIONFrom systems of record to systems that learn
+
From systems of record to systems that learn
How can operational experience become a durable cognitive asset?
ECS connects companion and task agents with skills, organizational knowledge, and persistent workspaces. KSTAR records can link decisions to their evidence, actions, outcomes, and subsequent knowledge updates.
04AI + X EDUCATIONAccelerated learning through human–AI symbiosis
+
Accelerated learning through human–AI symbiosis
What changes when learners have a companion that remembers their context and helps them take on more complex work?
This direction explores interdisciplinary transfer, experimentation, and meaningful human–AI tasks, with assessment focused on understanding and the ability to apply knowledge.
05COMPLEX SYSTEMSEmergence, persistence, and adaptive organization
+
Emergence, persistence, and adaptive organization
How do organized systems emerge, maintain themselves, and change across levels?
The research agenda connects multilevel causal structure, feedback, phase transitions, and recursive learning. Mathematical correspondence and empirical validation remain work to be developed.
Research agenda · These summaries describe developing ideas, not claims of completed empirical validation.
A connected inquiry into
intelligent systems.
Functorism is a research program by Dr. Richard Tong (佟佳睿), bringing together the philosophy of information, category-theoretic modeling, neuro-symbolic architectures, and human–AI collaboration.
The aim is to connect conceptual foundations with operational learning loops and practical agent systems—while keeping formal claims, architectural proposals, and open questions explicit.