9 papers
Approaching the Continuous from the Discrete: an Infinite Tensor Product Construction
Antonio Lorenzin, Fabio Zanasi
Increasingly in recent years, probabilistic computation has been investigated through the lenses of categorical algebra, especially via string diagrammatic calculi. Whereas categor…
A Diagrammatic Axiomatisation of Behavioural Distance of Nondeterministic Processes
Wojciech Różowski, Robin Piedeleu, Alexandra Silva +1
Behavioural distances provide a quantitative approach to comparing the states of transition systems, moving beyond traditional Boolean notions of equivalence. In this paper, we dev…
Complete Diagrammatic Axiomatisations of Relative Entropy
Ralph Sarkis, Fabio Zanasi
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In thi…
Layered Monoidal Theories II: Fibrational Semantics
Leo Lobski, Fabio Zanasi
Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models…
Layered Monoidal Theories I: Diagrammatic Algebra and Applications
Leo Lobski, Fabio Zanasi
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation…
Graded String Diagrams for Imprecise Probability and Causal Intervention
Ralph Sarkis, Fabio Zanasi
We introduce string diagrams for graded symmetric monoidal categories. Our approach includes a definition of graded monoidal theory and the corresponding freely generated syntactic…