Eigil Fjeldgren Rischel https://erischel.com/index/ index /index/ Eigil Fjeldgren Rischel false My name is Eigil Fjeldgren Rischel. I'm studying for a PhD in Computer and Information Sciences at the Mathematically Structured Programming group at the University of Strathclyde. My advisors are Neil Ghani and Radu Mardare. I mainly work on applications of category theory to probability and statistics. Eigil Fjeldgren Rischel https://erischel.com/efr-0032/ efr-0032 /efr-0032/ List of Publications Click to expand. Radu Mardare Neil Ghani Eigil Fjeldgren Rischel 2025 9 17 https://erischel.com/mardare-ghani-rischel-2025/ mardare-ghani-rischel-2025 /mardare-ghani-rischel-2025/ Metric Equational Theories Reference 10.4204/eptcs.428.11 Radu Mardare Neil Ghani Eigil Fjeldgren Rischel 2025 9 17 Abstract This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET) with the Enriched Lawvere Theories. We extend QETs to Metric Equational Theories (METs) where operations no longer have finite sets as arities (as in QETs and the general theory of universal algebras), but arities are now drawn from countable metric spaces. This extension is inspired by the theory of Enriched Lawvere Theories, which suggests that the arities of operations should be the lambda-presentable objects of the underlying lambda-accessible category. In this setting, the validity of terms in METs can no longer be guaranteed independently of the validity of equations, as is the case with QET. We solve this problem, and adapt the sound and complete proof system for QETs to these more general METs, taking advantage of the specific structure of metric spaces. Tobias Fritz Tomas Gonda Paolo Perrone Eigil Fjeldgren Rischel 2023 6 15 https://erischel.com/fritz-gonda-perrone-rischel-rep/ fritz-gonda-perrone-rischel-rep /fritz-gonda-perrone-rischel-rep/ Representable Markov categories and comparison of statistical experiments in categorical probability Reference 10.1016/j.tcs.2023.113896 Tobias Fritz Tomas Gonda Paolo Perrone Eigil Fjeldgren Rischel 2023 6 15 Abstract 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 conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay the foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads. Matteo Capucci Bruno Gavranović Jules Hedges Eigil Fjeldgren Rischel 2022 11 3 https://erischel.com/towards-cybercat/ towards-cybercat /towards-cybercat/ Towards Foundations of Categorical Cybernetics Reference 10.4204/EPTCS.372.17 Matteo Capucci Bruno Gavranović Jules Hedges Eigil Fjeldgren Rischel 2022 11 3 Abstract 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 is an optimiser such as gradient descent, and an approach to compositional game theory closely related to open games, in which the controller is a composite of game-theoretic agents. We believe that “cybernetic” is an appropriate name for the processes that can be described in this framework. Dylan Braithwaite Matteo Capucci Bruno Gavranović Jules Hedges Eigil Fjeldgren Rischel 2021 12 21 https://erischel.com/fibre-optics-2021/ fibre-optics-2021 /fibre-optics-2021/ Fibre optics Reference 10.48550/arXiv.2112.11145 http://arxiv.org/abs/2112.11145 Dylan Braithwaite Matteo Capucci Bruno Gavranović Jules Hedges Eigil Fjeldgren Rischel 2021 12 21 Abstract Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied category theory as models of bidirectional processes. From the definition of lenses over a finite product category, optics weaken the required structure to actions of monoidal categories, and dependent lenses make use of the additional property of finite completeness (or, in case of polynomials, even local cartesian closure). This has caused a split in the applied category theory literature between those using optics and those using dependent lenses. The goal of this paper is to unify optics with dependent lenses, by finding a definition of fibre optics admitting both as special cases. Eigil Fjeldgren Rischel Sebastian Weichwald 2021 8 5 https://erischel.com/rischel_compositional_2021/ rischel_compositional_2021 /rischel_compositional_2021/ Compositional abstraction error and a category of causal models Reference 10.48550/arXiv.2103.15758 http://arxiv.org/abs/2103.15758 Eigil Fjeldgren Rischel Sebastian Weichwald 2021 8 5 Abstract 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 move between the different joint distributions and make predictions about the variables upon intervening on the system. Yet, it is difficult to formalise how we may change the underlying variables used to describe the system, say moving from fine-grained to coarse-grained variables. Here, we argue that compositionality is a desideratum for such model transformations and the associated errors: When abstracting a reference model M iteratively, first obtaining M' and then further simplifying that to obtain M'', we expect the composite transformation from M to M'' to exist and its error to be bounded by the errors incurred by each individual transformation step. Category theory, the study of mathematical objects via compositional transformations between them, offers a natural language to develop our framework for model transformations and abstractions. We introduce a category of finite interventional causal models and, leveraging theory of enriched categories, prove the desired compositionality properties for our framework. Tobias Fritz Eigil Fjeldgren Rischel 2020 8 11 https://erischel.com/rischel-fritz-infinite-products/ rischel-fritz-infinite-products /rischel-fritz-infinite-products/ Infinite products and zero-one laws in categorical probability Reference 10.32408/compositionality-2-3 Tobias Fritz Eigil Fjeldgren Rischel 2020 8 11 Abstract We state and prove the zero-one laws of Kolmogorov and Hewitt-Savage within the setting of Markov categories, a category-theoretic approach to the foundations of probability and statistics. This gives general versions of these results which can be instantiated not only in measure-theoretic probability, where they specialize to the standard ones in the setting of standard Borel spaces, but also in other contexts. For example, applying the Kolmogorov law to the Kleisli category of the hyperspace monad on topological spaces gives criteria for when maps out of an infinite product of topological spaces into a Hausdorff space are constant. 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