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Attributed C-Sets as algebraic databases. Category-theoretic data structures generalizing graphs and dataframes with Gay.jl color integration.
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ACSets (Attributed C-Sets): Algebraic databases with Specter-style bidirectional navigation. Category-theoretic formalism for relational databases.
ACSets (Attributed C-Sets): Algebraic databases with Specter-style bidirectional
Bridge active inference theory with robot control using K-Scale's JAX/MuJoCo stack. Use when connecting predictive coding to locomotion policies, mapping KL divergence minimization to RL training, applying mean field approximation to robotics state estimation, or implementing sim2real as inference about future observations.
Implement affective valence as directional derivative of interoceptive energy landscapes for AI alignment. Use when building alignment-aware RL agents, validating GF(3) conservation in reward signals, training Langevin-based policies, or analyzing fold-change detection signals in POMDP environments.
Category-theoretic graph rewriting with DPO, SPO, and SqPO pushouts for C-Sets. Declarative transformation of acset data structures.
| name | acsets-hatchery |
| description | Attributed C-Sets as algebraic databases. Category-theoretic data structures generalizing graphs and dataframes with Gay.jl color integration. |
| metadata | {"trit":0,"color":"#E146A8"} |
ACSets.jl provides acsets ("attributed C-sets") - data structures generalizing both graphs and data frames. They are an efficient in-memory implementation of category-theoretic relational databases.
An ACSet is a functor from a category C to Set, with attributes. This means:
using ACSets
# Define a schema
@present SchGraph(FreeSchema) begin
V::Ob
E::Ob
src::Hom(E, V)
tgt::Hom(E, V)
end
# Create an acset
g = @acset Graph begin
V = 3
E = 2
src = [1, 2]
tgt = [2, 3]
end
# Rec2020 wide gamut with acset seed
gay_seed!(0xb4545686b9115a09)
# Mixed mode checkpointing
params = OkhslParameters()
∂params = Enzyme.gradient(Reverse, loss, params, seed)
Patterson, Lynch, Fairbanks. Categorical data structures for technical computing. Compositionality 4, 5 (2022). arXiv:2106.04703
0xb4545686b9115a09algebraic-rewriting (-1) ⊗ acsets-hatchery (0) ⊗ gay-monte-carlo (+1) = 0 ✓
acsets-algebraic-databases - Full ACSet guidespecter-acset - Bidirectional navigationworld-a - AlgebraicJulia ecosystem