Rewrite rules are organized via a graphical syntax into discrete-time simulations which can be understood as agent-based models. This representation is transparent, compositional, and serializable.| blog.algebraicjulia.org
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.| blog.algebraicjulia.org
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.| blog.algebraicjulia.org
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.| blog.algebraicjulia.org
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.| blog.algebraicjulia.org
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.| blog.algebraicjulia.org
In this post we unveil the category of attributed C-sets. It is an upgrade to the category of C-sets that makes each element of a component set (e.g. each vertex or edge in a graph) have attributes, which may be elements of arbitrary sets/Julia types. In order to formalize attributed C-sets, we also take a tour of double category theory and profunctors.| blog.algebraicjulia.org