# Working Paper: Towards Schema-based Learning from a Category-Theoretic Perspective

arXiv: https://arxiv.org/abs/2604.10589 · HTML: https://mlsanity.com/paper/2604.10589/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 3 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Builds on (most cited first, 1 of 1)

- [CertRL: Formalizing Convergence Proofs for Value and Policy Iteration in Coq](https://mlsanity.com/paper/2009.11403/) (2020)

## Abstract (arXiv)

We introduce a hierarchical categorical framework for Schema-Based Learning (SBL) structured across four interconnected levels. At the schema level, a free multicategory Schsyn encodes fundamental schemas and transformations. An implementation functor I maps syntactic schemas to representational languages, inducing via the Grothendieck construction the total category Schimpl. Implemented schemas are mapped by a functor Model into the Kleisli category KL(G) of the Giry monad, yielding probabilistic models, while an instances presheaf assigns evaluated instance spaces. A semantic category Schsem, defined as a full subcategory of KL(G), provides semantic grounding through an interpretation functor from Schimpl. At the agent level, Schimpl is equipped with a duoidal structure OSch supporting schema-based workflows. A left duoidal action on the category Mind enables workflow execution over mental objects, whose components include mental spaces, predictive models, and a cognitive kernel composed of memory and cognitive modules. Each module is specified by schema-typed interfaces, duoidal workflows, a success condition, and a logical signature. Memory is formalized categorically via memory subsystems, a presheaf DataM, a monoidal operation category OpsM, and read/write natural transformations. Together with the Body category, Mind defines the embodied SBL agent. At higher levels, SBL is represented as an object of the agent architecture category ArchCat, enabling comparison with heterogeneous paradigms, while the World category models multi-agent and agent-environment interactions. Altogether, the framework forms a weak hierarchical n-categorical structure linking schema semantics, cognition, embodiment, architectural abstraction, and world-level interaction.