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.