Categorical AGI Architectures

• ‘AGI architectures in a category’ are formal frameworks that treat cognitive functions as compositional objects to enable rigorous, mathematical comparisons.
• The approach employs hypergraph categories, profunctors, and diagrammatic syntax to distinguish between structural, informational, and semantic properties.
• Comparative case studies in RL, causal RL, and schema-based learning illustrate how varied feedback loops and knowledge organizations yield richer architectural insights.

Searching arXiv for papers on AGI architecture taxonomy and category-theoretic comparative frameworks. “AGI architectures in a category” denotes an emerging line of work that treats artificial general intelligence architectures not merely as implementations or benchmark-performing systems, but as compositional objects amenable to formal comparison, translation, and structural analysis. In this view, an architecture is characterized by how it organizes perception, memory, reasoning, action, control, and knowledge, and by the kinds of transformations that preserve or alter those organizations. The most explicit formulation appears in a 2026 position paper that proposes a category-theoretic comparative framework for architectures such as classical reinforcement learning (RL), causal RL (CRL), schema-based learning (SBL), and related paradigms (Riscos et al., 30 Mar 2026). Surrounding this formal program is a broader architectural literature that supplies the objects of comparison: hybrid discriminative–generative perceptual systems (Potapov et al., 2018), modular control-oriented AGI frameworks (Dollinger et al., 2024), heterogeneous system-design approaches (Kurshan, 2023), layered knowledge-preserving metamodels (Latapie et al., 2020), top-down cognitive architectures with universal knowledge models (Sukhobokov et al., 2024), concept-centered knowledge-graph architectures (Voss et al., 2023), system-level AGI decompositions into internal, interface, and infrastructure dimensions (Feng et al., 2024), categorical generative architectures based on simplicial structure (Mahadevan, 2024), and memory-centered bio-inspired proposals (Park, 5 Jun 2026). Taken together, these works define a research category in two senses: a taxonomy of AGI architectural families, and a mathematical ambition to represent those families within an explicit categorical framework.

1. Category-theoretic formulation of AGI architectures

The most direct formal treatment represents an AGI architecture as a structured triple

$A := (\mathcal{G}_A,\mathsf{Know}_A,\Phi_A),$

where $\mathcal{G}_A$ is a distinguished symmetric monoidal subcategory of a hypergraph category capturing admissible architectural diagrams, $\mathsf{Know}_A$ is a hypergraph category of knowledge structures and knowledge transformations, and $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$ is a profunctor relating architectural syntax to knowledge organization (Riscos et al., 30 Mar 2026). This construction makes an architecture into a theory of compositional interaction rather than a single algorithm. The syntax layer specifies allowed workflows among modules such as perception, action, update, and inference; the knowledge layer specifies the internal informational carriers and the transformations they admit; the profunctor links the two when that link is not functorial.

The use of hypergraph categories is deliberate. The framework adopts presentations of the form

$\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$

with interface types, primitive generators, and structural equations, and relies on symmetric monoidal structure together with special commutative Frobenius algebra structure for copying, merging, feedback, and diagrammatic wiring (Riscos et al., 30 Mar 2026). In this setting, an “architectural diagram” is a morphism in the syntactic subcategory, while a “knowledge workflow” is a morphism in the knowledge category.

Architecture morphisms are then defined as pairs of symmetric monoidal functors between syntax and knowledge layers, together with a natural transformation relating the profunctors. This permits formal statements of refinement, forgetful translation, and equivalence across architectures. The same paper further introduces a Grothendieck fibration

$p : Agents(\mathcal{E}) \to \mathbf{ArchAgents},$

where an agent is a semantic realization of an architecture in a target semantic category $\mathcal{E}$, and moving along an architecture morphism induces reindexing on agents (Riscos et al., 30 Mar 2026). This separates architecture-level questions from implementation-level questions while preserving a precise relation between them.

A central consequence is the distinction among structural, informational, and semantic properties. Structural properties are derivable judgments in the hypergraph presentation; informational properties depend on the organization of the knowledge category and the interpretation of generators into that category; semantic properties concern concrete implemented agents and are expressed by an institution

$$\mathcal{I}=(\mathbf{Sign},\mathbf{Sen},\mathbf{Mod},\models).$$

This yields a proof-carrying view of AGI architecture comparison: some claims are diagrammatic, some are knowledge-organizational, and some require semantic certification in realized systems (Riscos et al., 30 Mar 2026). This suggests that “AGI architectures in a category” is not merely metaphorical. It is a proposal for a formal comparative language in which architectural differences become statements about composition laws, informational ontology, and realizability.

2. Comparative expressivity: RL, causal RL, and schema-based learning

The comparative force of the categorical framework is illustrated through three case studies. Classical RL is described as minimal and centralized. Its syntactic types are

$S,\ A,\ E,\ \Theta,$

with generators

$$\mathsf{Policy} : S \otimes \Theta \to A,\qquad \mathsf{EnvInteraction} : S \otimes A \to E,\qquad \mathsf{Update} : \Theta \otimes E \to \Theta.$$

Its knowledge layer contains only a single persistent carrier $\mathcal{G}_A$0, and the profunctor relates only $\mathcal{G}_A$1 to itself (Riscos et al., 30 Mar 2026). Structurally, the architecture has a single global feedback loop and closure of persistent information into one undifferentiated state. The same source states that this makes RL architecturally unable to represent modular knowledge, causal abstraction, or selective reuse.

Causal RL enriches this organization by introducing separate policy and causal carriers,

$\mathcal{G}_A$2

and generators for policy update, causal update, and intervention. The architecture thereby acquires two coupled feedback loops, one for policy and one for causal modeling, linked through shared experience and intervention (Riscos et al., 30 Mar 2026). The key difference is not only additional functionality but a change in informational ontology: causal structure becomes an explicit internal object rather than an implicit parameterization.

Schema-based learning is presented as the most expressive of the three. It includes factorized observation and decision spaces, memory $\mathcal{G}_A$3, cognitive module identifiers $\mathcal{G}_A$4, families of model carriers, and generators such as

$\mathcal{G}_A$5

$\mathcal{G}_A$6

together with schema creation, deletion, combination, refinement, encapsulation, contextualization, and aggregation operators (Riscos et al., 30 Mar 2026). In this architecture, knowledge is modular, reusable, locally updatable, and partially isolated. Learning is not a primitive external update law but an emergent result of cognitive-module execution, observed through schema and memory changes.

A concise comparison is helpful.

Architecture	Persistent knowledge organization	Feedback structure
RL	Single global carrier $\mathcal{G}_A$7	One global loop
CRL	Policy carrier $\mathcal{G}_A$8 and causal carrier $\mathcal{G}_A$9	Two coupled loops
SBL	Families of schemas plus memory $\mathsf{Know}_A$0 and cognitive modules	Multiple local and mediated loops

This progression is important because it turns architectural comparison into a partially ordered enrichment story. The framework explicitly describes a stepwise path from CRL to SBL by factorizing interfaces, introducing multiple models, adding cognitive modules, adding memory, and inserting a body–mind mediation layer (Riscos et al., 30 Mar 2026). A plausible implication is that category-theoretic comparison does not merely classify existing architectures; it can express how one architecture is obtained from another by controlled relaxation or enrichment of structural constraints.

3. Architectural families supplying the comparison space

The categorical program presupposes a landscape of candidate architectures. Several papers articulate that landscape in non-categorical but structurally relevant terms. One recurring family is the modular, control-oriented architecture. The Open General Intelligence framework is presented as a macro design reference organized around three key components: Overall Macro Design Guidance, a Dynamic Processing System, and Framework Areas such as Executive Control, Autonomous Processing, Input/Output Integration, Short Term Memory, Long Term Memory, and Fabric Interconnect (Dollinger et al., 2024). Its weighting formalism,

$\mathsf{Know}_A$1

treats routing as a context-sensitive distribution over modules or actions. This is architecturally close to a control plane over specialized subsystems.

A second family is heterogeneous system design. The SAGI framework rejects a single universal AGI architecture and instead argues for a family of AGI systems spanning robotics to cloud-based large-scale systems, shaped jointly by alignment, energy, and system design (Kurshan, 2023). It explicitly distinguishes logicist, universalist, emergentist/connectionist, and hybrid approaches, while arguing that all remain incomplete without architecture-level integration of subsystems, hardware substrates, feedback loops, regulation, and moral processing. This positions AGI as a “system of systems.”

A third family is top-down cognitive architecture. The universal knowledge model and cognitive architecture for prototyping AGI surveys 42 cognitive architectures and proposes a design comprising input sensors, multimodal transformation into knowledge, consciousness, subconsciousness, goal management, problem statement, problem solving, learning, reflection, worldview, monitoring, emotional control, ethical assessments, social interaction, self-organization and meta-learning, multimodal output transformation, motor/manipulator command generation, and output devices, all connected through a Common knowledge bus (Sukhobokov et al., 2024). The same paper states that no reviewed architecture contained more than about 60% of the necessary functions as defined there.

A fourth family is knowledge-preserving layered architecture. The Deep Fusion Reasoning Engine treats knowledge as hierarchical structure and distinguishes antisymmetric relations as the backbone of knowledge from symmetric relations that add further structure (Latapie et al., 2020). Its DFRE Knowledge Graph is organized into levels $\mathsf{Know}_A$2, $\mathsf{Know}_A$3, $\mathsf{Know}_A$4, and $\mathsf{Know}_A$5, corresponding to raw data, symbolic/structural representation, higher abstraction, and goals such as self-monitoring, self-adjusting, and self-repair. The framework is orchestrated by an Agent and employs Focus of Attention to manage combinatorial explosion. In the reported retail experiment, overall accuracy rises from $\mathsf{Know}_A$6 without FoA to $\mathsf{Know}_A$7 with FoA (Latapie et al., 2020). The paper states that it does not provide explicit category theory, but it does provide strong category-like support through layered structure-preserving transformations.

A fifth family is concept-centered cognitive architecture. “Concepts is All You Need” argues for an integrated Cognitive AI architecture built around a high-performance knowledge graph/vector datastore supporting perception, memory, learning, inference, language, abstraction, and action (Voss et al., 2023). The central representational ladder is features, percepts, concepts, and abstract concepts, with concepts represented as vectors with a schema. The paper positions this as a third-wave cognitive architecture and reports a late-August 2023 benchmark with 419 natural-language statements and 737 questions, with reported scores of $\mathsf{Know}_A$8 for AIGO, $\mathsf{Know}_A$9 for Claude 2, and less than $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$0 for GPT-4 on that test (Voss et al., 2023).

A sixth family is layered full-stack AGI architecture. A 2024 survey decomposes AGI into internal, interface, and system dimensions, with internal components of perception, memory, reasoning, and metacognition; interfaces to the digital world, physical world, other AI agents, and humans; and system concerns spanning scalable model architectures, training, inference, efficiency, and computing platforms (Feng et al., 2024). This formulation does not formalize a category, but it provides a high-level decomposition of the architectural object to be compared.

These families populate the comparison space that a categorical framework seeks to organize. They differ primarily in how they factor cognition, control, knowledge, and interaction.

4. Perception, generation, memory, and knowledge as categorical axes

The perception paper “Vision System for AGI” supplies a particularly clear architectural axis: the relation between discriminative inference and generative modeling (Potapov et al., 2018). It formalizes perception through latent state $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$1, transition prior $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$2, and observation model $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$3, with the perceptual task understood as posterior inference over $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$4 from current observations and temporal priors. The paper states that “the task of perception can be reduced to (1), although the task of learning the models should also be accounted for,” and argues that “Ultimately, it is necessary to state the task of vision as a task of reconstruction of a latent description of a scene within a trainable generative model” (Potapov et al., 2018). Its key architectural claim is that discriminative models are efficient but narrow, whereas generative models support explanation, unsupervised learning, one-shot learning, and transfer; viable AGI vision therefore requires a tightly coupled hybrid architecture rather than either component in isolation.

Memory is another axis that repeatedly appears as architecturally fundamental. In the vision paper, perception is distinguished from memory, but the estimation of the visible part of $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$5 is said to “intensively use $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$6, i.e. both read and update the memory” (Potapov et al., 2018). OGI separates Short Term Memory and Long Term Memory but treats them as overlapping and interconnected rather than strictly linear modules (Dollinger et al., 2024). DFRE introduces $$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$7 as a goal/motivation layer and supports cumulative, distributed, and federated learning over knowledge graphs (Latapie et al., 2020). The internal/interface/system survey elevates memory to one of the four central components of AGI Internal (Feng et al., 2024).

The strongest memory-centered claim appears in a 2026 position paper arguing that explicit memory is the cornerstone for AGI (Park, 5 Jun 2026). It proposes a memory module

$$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$8

with sparse indexing

$$\Phi_A : \mathcal{G}_A \nrightarrow \mathsf{Know}_A$$9

associative pattern completion, dynamic updates, one-shot storage, and adaptive forgetting (Park, 5 Jun 2026). The paper’s thesis is that LLMs are analogous to implicit memory, while long-horizon planning, metacognition, and symbolic reasoning depend on hippocampal explicit memory. This supplies an additional categorical axis: whether persistent knowledge is monolithic, role-split, schema-local, graph-structured, or explicitly episodic and associative.

Knowledge representation itself constitutes another axis. DFRE’s distinction between antisymmetric and symmetric relations, its layered $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$0 hierarchy, and its insistence that confusing abstraction levels is knowledge-corrupting are explicitly described as category-like but not category-theoretic (Latapie et al., 2020). The universal knowledge model proposes archigraphs extending annotated metagraphs to represent unformalized, partially formalized, and formalized knowledge in one substrate, including text, images, audio, video, graphs, algorithms, databases, neural networks, ontologies, frames, and predicate-calculus models (Sukhobokov et al., 2024). A plausible implication is that category-theoretic comparison could treat these knowledge substrates as differing $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$1 components even when their control layers remain similar.

5. Simplicial and categorical generative architectures

Category-theoretic treatments are not confined to comparative meta-frameworks. GAIA proposes a generative AI architecture in which modules are organized as a simplicial complex rather than a sequential chain (Mahadevan, 2024). Its top layer is the simplicial category $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$2, its middle layer contains model families treated as categories or universal coalgebras, and its bottom layer is a category of elements over data. A simplicial set

$\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$3

provides graded collections $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$4 with face and degeneracy maps. In this architecture, higher-dimensional simplices mediate multiscale information flow, so learning is not only forward and backward along a line but recursive across simplicial strata.

GAIA formulates learning as a lifting problem. Given a commutative square, learning consists in finding a diagonal filler that makes the relevant equations hold (Mahadevan, 2024). Horns $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$5 represent partially specified simplices with one face missing. The inner horn $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$6 corresponds to composition, while outer horns $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$7 and $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$8 correspond to inverse-like problems. This reframes architectural competence in terms of which lifting problems the system can solve. If every horn has a filler, the simplicial set is a Kan complex. The paper treats that as an idealized setting of rich learning and inference.

The same paper reformulates backpropagation in compositional and coalgebraic terms. It reviews the standard learner 4-tuple $\mathsf{Hyp}\langle Types, Gen \mid Eq \rangle,$9, composition of learners, and a functor

$p : Agents(\mathcal{E}) \to \mathbf{ArchAgents},$0

then advances the stronger claim that backpropagation is better understood as an endofunctor on parameter space itself, with

$p : Agents(\mathcal{E}) \to \mathbf{ArchAgents},$1

This yields a coalgebraic model of learning dynamics and, with a stochastic variant $p : Agents(\mathcal{E}) \to \mathbf{ArchAgents},$2, a probabilistic coalgebra (Mahadevan, 2024). The paper further invokes ends and coends, interpreting ends as probabilistic generative models and coends as topological generative models.

Relative to the comparative framework of $p : Agents(\mathcal{E}) \to \mathbf{ArchAgents},$3, GAIA operates at a different level. It proposes an architecture inside category theory rather than a category-theoretic language for comparing architectures. Yet the two are closely aligned in methodological intent. Both treat architecture as structured composition, both separate syntax from realization, and both emphasize that sequential composition is insufficient to capture richer organizational forms (Mahadevan, 2024, Riscos et al., 30 Mar 2026). This suggests convergence between applied categorical design and categorical metatheory for AGI.

6. Taxonomic significance, controversies, and open problems

Across these papers, three recurring theses define the taxonomic significance of “AGI architectures in a category.” First, AGI is increasingly treated as an architectural problem rather than solely a scaling problem. SAGI states that the leap from narrow AI to AGI requires multiple functional subsystems in a balanced, integrated, and controllable architecture, with alignment and energy as first-class architectural constraints (Kurshan, 2023). OGI similarly argues that current AI is too siloed, single-modal, and statically routed, and proposes modular subsystems linked by a dynamic processing system and fabric interconnect (Dollinger et al., 2024). The internal/interface/system survey says explicitly that AGI is a full-stack problem involving mind, world interface, and infrastructure (Feng et al., 2024).

Second, multiple architectural categories are now visible. These include monolithic parameter-carrier architectures, causal-split architectures, schema-modular architectures, hybrid discriminative–generative perceptual architectures, knowledge-graph and metamodel architectures, macro-modular control architectures, concept-centered cognitive architectures, and bio-inspired explicit-memory architectures (Potapov et al., 2018, Latapie et al., 2020, Voss et al., 2023, Kurshan, 2023, Dollinger et al., 2024, Park, 5 Jun 2026). The 2026 categorical framework provides a common comparative language for some of these differences, especially those concerning wiring discipline, persistent information carriers, modularity, and feedback (Riscos et al., 30 Mar 2026).

Third, the formal program remains incomplete. The category-theoretic comparative paper explicitly identifies immediate future work: making architecture morphisms more explicit, formalizing the category or preorder of properties, refining the ontology of types, and adding algebraic theories over architectures for laws such as Bellman equations or Bayes rules (Riscos et al., 30 Mar 2026). It also introduces an extended architecture

$p : Agents(\mathcal{E}) \to \mathbf{ArchAgents},$4

with an explicit constraint layer $p : Agents(\mathcal{E}) \to \mathbf{ArchAgents},$5 to capture Bellman consistency, Markov admissibility, factorization requirements, type ontology, and interface constraints without conflating them with free diagrammatic syntax (Riscos et al., 30 Mar 2026). That addition is significant because many practically important architectural constraints are not naturally expressible as equations in a hypergraph presentation.

Several controversies are objective and recurrent. One concerns universal versus heterogeneous architecture. SAGI explicitly rejects a single universal AGI architecture in favor of a family of application-specific systems (Kurshan, 2023), whereas the categorical comparative framework seeks a universal language for comparison rather than a universal architecture (Riscos et al., 30 Mar 2026). These positions are compatible, but only if “universal” is reserved for metatheory rather than design prescription. Another concerns the role of LLMs. The internal/interface/system survey treats LLMs as the present general-purpose backbone but not the whole architecture (Feng et al., 2024), while the explicit-memory paper argues that LLM-like implicit learning cannot by itself produce the higher-order cognition associated with AGI (Park, 5 Jun 2026). A third concerns the role of strong priors. The AGI vision paper calls the strength of priors “really controversial,” balancing tractability against generality (Potapov et al., 2018).

The present state of the field therefore combines a broad architectural taxonomy with an early formal comparative apparatus. The categorical turn does not yet deliver a complete theory of AGI, nor does it settle which architecture class is sufficient for AGI. What it does provide is a disciplined way to state architectural differences: centralized versus factorized knowledge, single versus coupled versus distributed feedback loops, monolithic versus schema-local update, feedforward versus bidirectional or generative reconstruction, static versus dynamic routing, and parametric memory versus explicit memory. This suggests that the phrase “AGI architectures in a category” names a developing research program whose core objective is to make such differences mathematically comparable without collapsing them into performance-only benchmarks (Riscos et al., 30 Mar 2026).