String diagrams are a powerful and intuitive graphical syntax, originating in theoretical
physics and later formalised in the context of symmetric monoidal categories. In recent …

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

We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum
theory in odd prime dimensions. These calculi recover many of the nice features of the qubit …

How do spaces in physics emerge from pregeometric discrete building blocks governed by
computational rules? To address this question we investigate non-deterministic rewriting …

This thesis develops the translation between category theory and computational linguistics
as a foundation for natural language processing. The three chapters deal with syntax …

We investigate algebraic and compositional properties of abstract multiway rewriting
systems, which are archetypical structures underlying the formalism of the Wolfram model …

In this paper, we address the problem of proving confluence for string diagram rewriting,
which was previously shown to be characterised combinatorially as double-pushout …

This paper develops a formal string diagram language for monoidal closed categories.
Previous work has shown that string diagrams for freely generated symmetric monoidal …

We introduce a mathematical framework for retrosynthetic analysis, an important research
method in synthetic chemistry. Our approach represents molecules and their interaction …

Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes,
connecting computational mathematics to higher categories and homotopy theory: the two …