Mathematics - Category Theory

Artificial IntelligenceTeaching Robots Through Compositional Reinforcement Learning

Learn how breaking tasks helps robots train efficiently.

Georgios Bakirtzis, Michail Savvas, Ruihan Zhao

Jun 17, 2025 ― 8 min read

Category TheoryAn Introduction to Functor Double Categories

Explore functor double categories and their role in understanding complex relationships in mathematics.

Jaco Ruit

Jun 16, 2025 ― 5 min read

CombinatoricsUnderstanding Graph Structures and Their Uses

A look into graphs, their properties, and practical applications.

Benjamin Merlin Bumpus, James Fairbanks, Will J. Turner

Jun 16, 2025 ― 4 min read

High Energy Physics - TheoryThe Impact of Boundary Conditions in Quantum Theories

Exploring boundary conditions and their role in quantum systems with categorical symmetries.

Lakshya Bhardwaj, Christian Copetti, Daniel Pajer

Jun 15, 2025 ― 7 min read

Category TheoryFibrations in Mathematics: An Overview

A look into the concept and applications of fibrations in mathematics.

Danel Ahman, Greta Coraglia, Davide Castelnovo

Jun 15, 2025 ― 5 min read

Category TheoryRozansky-Witten Models and Functorial Field Theory

Exploring Rozansky-Witten models and their significance in mathematics and physics.

Lorenzo Riva

Jun 14, 2025 ― 4 min read

Category TheoryUnderstanding 3-Manifolds through Fusion Categories

A look into the study of complex three-dimensional shapes.

Fabio Lischka

Jun 14, 2025 ― 5 min read

Category TheoryBridging Mathematics: Categorical Galois Theory

A look into the links between Galois theory and category theory.

Joseph Rennie

Jun 11, 2025 ― 6 min read

Category TheoryUnderstanding Functions and Their Changes

A look into functions, derivatives, and their interconnectedness in everyday scenarios.

Matteo Capucci, Geoffrey S. H. Cruttwell, Neil Ghani

Jun 9, 2025 ― 5 min read

Category TheoryUnderstanding Multivariate Functors in Mathematics

An overview of multivariate functors and their significance in mathematical analysis.

Robert Paré

Jun 7, 2025 ― 5 min read

Category TheoryPropositional Equality in Type Theory: A Deeper Look

Examining propositional equality's role in type theory and its implications.

Andrea Laretto, Fosco Loregian, Niccolò Veltri

Jun 6, 2025 ― 4 min read

Quantum AlgebraCommutative Algebras and Their Role in Mathematics

An overview of commutative algebras and their applications in advanced mathematical contexts.

Thomas Creutzig, Robert McRae, Kenichi Shimizu

Jun 5, 2025 ― 5 min read

Logic in Computer ScienceGuarded Recursion in Programming Languages

Exploring how guarded recursion enhances infinite data structures in programming.

Louis Lemonnier

Jun 3, 2025 ― 9 min read

Category TheoryConnecting Topology and Algebra: The Gelfand-Naimark Theorem

A look at the Gelfand-Naimark Theorem linking topology and algebra.

Sebastian Alvarez Avendaño, Breitner Ocampo, Pedro Rizzo

Jun 3, 2025 ― 6 min read

Category TheoryUnderstanding Giry Algebras in Polish Spaces

This article explains Giry algebras and their role in probability and Polish spaces.

Kirk Sturtz

Jun 3, 2025 ― 5 min read

General EconomicsInnovation Through Combination: A Simple Approach

Combining existing ideas leads to effective business innovation.

Jürgen Jost, Massimo Warglien

Jun 2, 2025 ― 7 min read

Category TheoryUnderstanding the Quillen Negation Monoid in Category Theory

A look at how the Quillen negation monoid shapes morphism properties in category theory.

Misha Gavrilovich, Misha Rabinovich

May 31, 2025 ― 5 min read

Mathematical PhysicsThe Intricacies of Symmetry in Quantum Physics

An overview of how symmetries and observables interact in quantum mechanics.

Thomas Bartsch

May 26, 2025 ― 8 min read

Algebraic TopologyExploring the Dynamics of Modules in Algebra

A look into modules, their types, and how they interact in algebra.

Alex Elchesen, Amit Patel

May 25, 2025 ― 7 min read

Category TheoryUnderstanding Ghosts in Mathematics

Explore the intriguing concepts of ghost maps and ideals in algebra.

S. Estrada, X. H. Fu, I. Herzog

May 24, 2025 ― 6 min read

Category TheoryUsing Computers to Understand Category Theory

A look at computational methods in category theory and their applications.

Simon Forest

May 23, 2025 ― 7 min read

Rings and AlgebrasUnderstanding DRC-Semigroups: A Guide

Learn about DRC-semigroups and their importance in mathematics and technology.

James East, Matthias Fresacher, P. A. Azeef Muhammed

May 22, 2025 ― 4 min read

Category TheoryUnderstanding Modest Sets and Partial Equivalence Relations

A simple guide to modest sets and partial equivalence relations.

Rahul Chhabra

May 18, 2025 ― 4 min read

Category TheoryOrganizing Game Night: A Mathematical Approach

Learn to arrange game night with concepts from monoidal bicategories.

Ettore Aldrovandi, Milind Gunjal

May 15, 2025 ― 6 min read

Algebraic TopologyUnderstanding Homotopy Theory Through Model and Diagram Categories

A look into model categories, diagram categories, and their applications in mathematics.

Boris Chorny, David White

May 15, 2025 ― 5 min read

General TopologyThe Connection Between Compact Spaces and Lattices

Discover how compact spaces and lattices interact in mathematics.

Elena Pozzan, Matteo Viale

May 9, 2025 ― 9 min read

Category TheoryUnderstanding Independence in Mathematics

A simple look at the concept of independence in math.

Mark Kamsma, Jiří Rosický

May 5, 2025 ― 7 min read

Logic in Computer ScienceConnecting Shapes: The Role of Colimits

A friendly exploration of colimits and their connections in homotopy type theory.

Perry Hart, Kuen-Bang Hou

May 5, 2025 ― 5 min read

Representation TheoryWeyl Modules: An Insightful Look into Representation Theory

Discover Weyl modules and their significance in algebraic structures.

Vladimir Dotsenko, Sergey Mozgovoy

Apr 30, 2025 ― 4 min read

Category TheoryUnderstanding Commutative Diagrams and Extensions in Mathematics

Explore the basics of commutative diagrams and their extensions in math.

Sébastien Mattenet, Tim Van der Linden, Raphaël M. Jungers

Apr 30, 2025 ― 7 min read

Representation TheoryUnlocking the Secrets of Perverse Sheaves

Dive into the intriguing world of perverse sheaves and their role in mathematics.

Mikhail Kapranov, Vadim Schechtman, Olivier Schiffmann

Apr 13, 2025 ― 6 min read

Logic in Computer ScienceUnlocking the Secrets of Type Theory

Explore higher identity proofs and their impact on programming and mathematics.

Thibaut Benjamin

Apr 11, 2025 ― 6 min read

Algebraic GeometryDemystifying Commutative Diagrams and Functors

Discover how commutative diagrams and functors simplify complex mathematical concepts.

Chirantan Chowdhury

Apr 4, 2025 ― 4 min read

Algebraic TopologyUnpacking Topology: Compactness and Finiteness

Discover the intriguing world of topology through compactness and finiteness.

Marco Volpe

Apr 2, 2025 ― 6 min read

Computer Vision and Pattern RecognitionPoset Filters: Enhancing Neural Network Performance

Uncover how poset filters improve neural networks by organizing data efficiently.

Eric Dolores-Cuenca, Aldo Guzman-Saenz, Sangil Kim

Mar 25, 2025 ― 7 min read

Category TheoryExploring Two-Dimensional Category Theory

Discover the fascinating interactions in two-dimensional category theory.

Nathanael Arkor, John Bourke, Joanna Ko

Mar 19, 2025 ― 5 min read

Category TheoryUnlocking the Secrets of Relational Doctrines

Discover how relational doctrines simplify complex relationships in math and life.

Francesco Dagnino, Fabio Pasquali

Mar 3, 2025 ― 5 min read

Quantum AlgebraA Culinary Journey Through Mathematics

Explore the delicious world of compact semisimple tensor categories.

Thibault D. Décoppet, Sean Sanford

Feb 18, 2025 ― 5 min read

Dynamical SystemsUnderstanding Dynamical Systems Through Data

Discover how data helps us interpret the changes in dynamical systems.

Suddhasattwa Das, Tomoharu Suda

Jan 27, 2025 ― 8 min read

Category TheoryUntangling the World of Circuit Algebras

A deep dive into circuit algebras and their real-world applications.

Sophie Raynor

Jan 25, 2025 ― 9 min read