Conceptual fragmentation is when a term assumed to have one meaning is found to have
many. When these different definitions overlap in meaning and application confusion and …

Markov categories are a recent categorical approach to the mathematical foundations of
probability and statistics. Here, this approach is advanced by stating and proving equivalent …

Categorical probability has recently seen significant advances through the formalism of
Markov categories, within which several classical theorems have been proven in entirely …

Interventional causal models describe several joint distributions over some variables used to
describe a system, one for each intervention setting. They provide a formal recipe for how to …

Markov categories have recently turned out to be a powerful high-level framework for
probability and statistics. They accomodate purely categorical definitions of notions like …

We make a formal analogy between random sampling and fresh name generation. We show
that quasi-Borel spaces, a model for probabilistic programming, can soundly interpret the ν …

Regulatory networks depict promoting or inhibiting interactions between molecules in a
biochemical system. We introduce a category-theoretic formalism for regulatory networks …

The categorified theories known as “doctrines” specify a category equipped with extra
structure, analogous to how ordinary theories specify a set with extra structure. We introduce …

Structured and decorated cospans are broadly applicable frameworks for building
bicategories or double categories of open systems. We streamline and generalize these …

Building on work of Rubenstein et al, we consider a notion of structurepreserving
transformations between structural causal models. We describe a category, in the sense of …