28 citations · 77 across the 9 of their papers we have counts for
9 papers
Clock systems for stochastic and non-deterministic categorical systems theories
Owen Lynch, David Jaz Myers, Eigil Fjeldgren Rischel +1
One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form…
Convex Duality Made Difficult
Eigil Fjeldgren Rischel
The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of…
The Universal Property of Measure-Theoretic Probability
Eigil Fjeldgren Rischel
Building on work of Chen, we give a universal property of the Markov category BorelStoch of standard Borel spaces and Markov kernels between them. To do this, we introduce a new no…
Metric Equational Theories
Radu Mardare, Neil Ghani, Eigil Rischel
This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET)…
Fibre optics
Dylan Braithwaite, Matteo Capucci, Bruno Gavranović +2
Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied categor…
Towards Foundations of Categorical Cybernetics
Matteo Capucci, Bruno Gavranović, Jules Hedges +1
We propose a categorical framework for processes which interact bidirectionally with both an environment and a 'controller'. Examples include open learners, in which the controller…
Compositional Abstraction Error and a Category of Causal Models
Eigil F. Rischel, Sebastian Weichwald
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…
Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability
Tobias Fritz, Tomáš Gonda, Paolo Perrone +1
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…
Infinite products and zero-one laws in categorical probability
Tobias Fritz, Eigil Fjeldgren Rischel
Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and…