Software

Much of our research is released as software. These packages are open source and developed in collaboration with the AlgebraicJulia team, including Evan Patterson’s group at the Topos Institute. The names on each card are the lab members, past and present, who work on it.

A decapode: three variables joined by the exterior derivative, the codifferential and the time derivative

Decapodes.jl

Compose and simulate multiphysics systems from diagrams of PDEs.

Luke Morris George Rauta Matt Cuffaro James Fairbanks

Vector-space stalks drawn as planes standing over the vertices and edges of a graph

CellularSheaves.jl

Cellular sheaves and sheaf Laplacians, used for multi-agent coordination.

James Fairbanks Tyler Hanks Itay Kadosh

An undirected wiring diagram: three objective boxes wired to shared junctions, with two outer ports

AlgebraicOptimization.jl

Compositional optimization: assemble large problems from small ones.

Tyler Hanks Samuel Cohen Trevor Gross

Gradient flow and its Euler discretisation, drawn as a chain of functors over a contour plot and a stream plot

AlgebraicControl.jl

Optimal control, compositionally.

A graph on eight vertices beside the clique tree that decomposes it

CliqueTrees.jl

Tree decompositions and chordal completions, underpinning sparse linear solves.

Richard Samuelson

Three bags, each holding a graph, joined by three adhesions whose vertices map into the bags along dotted spans

StructuredDecompositions.jl

Structured decompositions for compositional algorithms on graphs.

Benjamin Merlin Bumpus Richard Samuelson

Catlab.jl

The applied category theory framework the rest of the ecosystem builds on.

Kris Brown Micah Halter James Fairbanks Matt Cuffaro

The discrete de Rham complex on a triangulated patch: a value on every vertex, then on every directed edge, then on every face

CombinatorialSpaces.jl

Simplicial sets and the discrete exterior calculus.

Luke Morris George Rauta

Six populations of a composed ecosystem oscillating out of phase

AlgebraicDynamics.jl

Building dynamical systems compositionally.

James Fairbanks Matt Cuffaro Tyler Hanks Joana Bou Barcelo Wilmer Leal

Four rings joined in a cycle by four colored arrows, the objects and morphisms of a commutative square

ACSets.jl

Algebraic databases as in-memory data structures.

Kris Brown Luke Morris Matt Cuffaro James Fairbanks

GATlab.jl

A computer algebra system based on generalized algebraic theories.

Kris Brown Matt Cuffaro

An SIR Petri net: three species as circles, two transitions as squares, with infection drawing on the infected population

AlgebraicPetri.jl

Build Petri net models compositionally.

Micah Halter James Fairbanks