In the previous post, we defined a general approach for composing dynamical systems based on the mathematics of operads and operad algebras. In this post, we explore an undirected composition syntax in which dynamical systems compose by sharing resources. We also get a taste of hierarchical composition, i.e. composing systems which are themselves composites ..read more

It's breakfast time! You wake up and walk to your kitchen and notice a loaf of bread, a knife, a raw egg (in its shell), a skillet, and a stove burner sitting on the counter. You're hungry and your preferred state of existence is to, instead, have an egg sandwich sitting on your counter. You are saddened by the situation, but feel empowered to change it! You compare what you have and what you want, recall what cooking skills you have, and devise the following steps ..read more

For graphs and C-sets more generally, the most useful notion of equivalence differs from strict equality of the underlying data structures. Finding automorphism classes of C-sets addresses this problem; we explore how to compute automorphism classes and applications of them ..read more

Nonclassical logics are often thought to be abstruse and exotic, but they arise naturally as the logic of connected spaces. In this post, we introduce the propositional logic of subgraphs, and more generally of sub-C-sets, and illustrate it with computational examples. The nonclassicality of this logic is seen to be not just natural but inevitable, and also surprisingly useful ..read more

The chase in an algorithm in the context of databases that has applications in Catlab for model exploration, term rewriting, and enforcing schema axioms ..read more

Reflexive graphs are graphs where every vertex has a distinguished self-loop. While this may seem inconsequential, reflexive graphs have interestingly different properties than ordinary graphs owing to their different morphisms. We will see that reflexive graphs are more geometrical than graphs and also review the general notion of homomorphism between C-sets ..read more

Not just useful for graphs, C-sets are a general-purpose tool for data analysis offering the functionality of an in-memory relational database. In this post, we illustrate Catlab's new capabilities for querying C-sets and we explain the categorical underpinnings of conjunctive queries ..read more

Informally, many models are specified as compositions of primitive dynamical systems. In this series of posts, we make this modular specification formal by introducing a computing framework from composing open dynamical systems. In this first post of the series, we examine directed theories for composition ..read more

Structured cospans are a categorical method for turning closed systems into open ones. We show how structured cospans of Petri nets can be used to construct complex epidemiological models in a compositional way ..read more

We present an approach to scientific data management that utilizes category theory to seamlessly integrate workflow creation, database generation, and database querying. We use Catlab as a backend to provide this more continuous and consistent database experience ..read more