String diagrams are powerful graphical methods for reasoning in elementary category
theory. Written in an informal expository style, this book provides a self-contained …

This paper is a 'spiritual child'of the 2005 lecture notes Kindergarten Quantum Mechanics
Coecke (2005)[24], which showed how a simple, pictorial extension of Dirac notation …

We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the
calculus of binary relations that has the same expressivity as first order logic and comes with …

We investigate causal computations, which take sequences of inputs to sequences of
outputs such that the nth output depends on the first n inputs only. We model these in …

We introduce a general diagrammatic theory of digital circuits, based on connections
between monoidal categories and graph rewriting. The main achievement of the paper is …

Signal flow graphs are combinatorial models for linear dynamical systems, playing a
foundational role in control theory and engineering. In this survey, we overview a series of …

We describe categorical models of a circuit-based (quantum) functional programming
language. We show that enriched categories play a crucial role. Following earlier work on …

This paper addresses the question “what is a digital circuit?” in relation to the fundamentally
analog nature of actual (physical) circuits. A simple informal definition is given and then …

We study the relationship between cartesian bicategories and a specialisation of Lawvere's
hyperdoctrines, namely elementary existential doctrines. Both provide different ways of …

Constructor theory is a meta-theoretic approach that seeks to characterise concrete theories
of physics in terms of the (im) possibility to implement certain abstract" tasks" by means of …