Related papers: DisCoPy: Monoidal Categories in Python

We introduce a dialect of the Asynchronous pi-calculus, called AWpi, in which (1) an input name may be owned, at any time, by at most one process; (2) each name has either only the input or only the output capability. As a result, special…

We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a…

Building meaningful interoperation with external software units requires performing the conceptual interoperability analysis that starts with identifying the conceptual interoperability constraints of each software unit, then it compares…

We present a formalization in Lean 4, within the framework of the mathematical library Mathlib, of the unbiasing process for symmetric monoidal categories. This is realized by extending the data of a symmetric monoidal category to a…

Most application development happens in the context of complex APIs; reference documentation for APIs has grown tremendously in variety, complexity, and volume, and can be difficult to navigate. There is a growing need to develop…

We have built an open-source software system for the modeling of biomolecular reaction networks, SloppyCell, which is written in Python and makes substantial use of third-party libraries for numerics, visualization, and parallel…

Recent releases of open-source research codes and solvers for numerically solving partial differential equations in Python present a great opportunity for educators to integrate these codes into the classroom in a variety of ways. The ease…

Fong developed `decorated cospans' to model various kinds of open systems: that is, systems with inputs and outputs. In this framework, open systems are seen as the morphisms of a category and can be composed as such, allowing larger open…

These are lectures notes for a mini-course given at the conference Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras, and Categorification in June 2018. The goal is to introduce the reader to string diagram…

In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…

Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory,…

We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation,…

BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of…

Differential categories were introduced to provide a minimal categorical doctrine for differential linear logic. Here we revisit the formalism and, in particular, examine the two different approaches to defining differentiation which were…

This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…

A holographic microscope captures interference patterns, or holograms, that encode three-dimensional (3D) information about the object being viewed. Computation is essential to extracting that 3D information. By wrapping low-level…

Extracting actionable insight from complex unlabeled scientific data is an open challenge and key to unlocking data-driven discovery in science. Complementary and alternative to supervised machine learning approaches, unsupervised…

This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support…

We present an open-source simulation framework for optically detected magnetic resonance, developed in Python. The framework allows users to construct, manipulate, and evolve multipartite quantum systems that consist of spins and electronic…

Recently, there has been renewed interest in the theory and applications of de Paiva's dialectica categories and their relationship to the category of polynomial functors. Both fall under the theory of generalized polynomial categories,…