As the complexity and heterogeneity of a system grows, the challenge of specifying,
documenting and synthesizing correct, machine-readable designs increases dramatically …

We introduce DisCoPy, an open source toolbox for computing with monoidal categories. The
library provides an intuitive syntax for defining string diagrams and monoidal functors. Its …

This document is an elementary introduction to string diagrams. It takes a computer science
perspective: rather than using category theory as a starting point, we build on intuitions from …

Contemporary proof assistants rely on complex automation and process libraries with
millions of lines of code. At these scales, understanding the emergent interactions between …

String diagrams turn algebraic equations into topological moves that have recurring shapes,
involving the sliding of one diagram past another. We individuate, at the root of this fact, the …

We introduce a dependent type theory whose models are weak ω-categories, generalizing
Brunerie's definition of ω-groupoids. Our type theory is based on the definition of ω …

Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them
suitable to express resource-sensitive systems, in which variables cannot be copied or …

Opetopes are algebraic descriptions of shapes corresponding to compositions in higher
dimensions. As such, they offer an approach to higher-dimensional algebraic structures, and …

This thesis introduces quantum natural language processing (QNLP) models based on a
simple yet powerful analogy between computational linguistics and quantum mechanics …

We enhance the calculus of string diagrams for monoidal categories with hierarchical
features in order to capture closed monoidal (and cartesian closed) structure. Using this new …