Topos Institute Courses

Polynomial Interfaces - Applied Category Theory and User Interface Design

Explore how applied category theory connects to user interface design through monads, comonads, and polynomial functors, with insights into the Semagrams library implementation.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Totally Live Programming and Proving in Hazel - A Programming Environment Overview

Explore the Hazel programming environment's innovative approach to live programming, error handling, and theorem proving through hands-on demonstrations and theoretical insights.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

How to Make Mathematicians Into Programmers and Vice Versa

Explore the intersection of formalized mathematics and programming through cognitive science, examining how to improve tools and education for both mathematicians and developers.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Generalization of Inversion Using Bayes' Rule with Applications to Quantum Systems

Delve into categorical definitions of Bayesian inversion, exploring its applications in quantum systems and semi-cartesian categories through string diagrams and theoretical frameworks.

• YouTube
• 59 minutes
• On-Demand
• Free Video

All Concepts are Essentially Algebraic - A Study of Dependently-Typed Algebraic Theories

Delve into the mathematical exploration of how dependently-typed algebraic theories can unify and describe complex mathematical structures, from groups to entire mathematical universes.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Communicating Relational Thinking Through Category Theory and Mathematics

Explore the innovative approach to teaching categorical thinking through an open-source textbook, focusing on making abstract mathematical concepts accessible to broader STEM audiences.

• YouTube
• 53 minutes
• On-Demand
• Free Video

From GS-Monoidal to Cartesian Categories - A Structural Analysis

Delve into the structural relationships between cartesian and symmetric monoidal categories, exploring natural transformations, gs-monoidal taxonomies, and category theory fundamentals.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Topological Data Analysis of Spatial Systems

Explore topological data analysis through real-world applications, from voting patterns to spider web structures, using persistent homology to uncover hidden patterns in spatial data.

• YouTube
• 1 hour
• On-Demand
• Free Video

Parametric Profunctor Preoptics in Neural Networks and Haskell Implementation

Dive into advanced category theory concepts, exploring parametric optics and profunctors for neural network implementation, with practical applications in Haskell programming.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Three Toposes for Probability and Randomness

Explore three innovative toposes that revolutionize probabilistic reasoning, random variables, and synthetic probability theory, offering new perspectives on measurability and randomness.

• YouTube
• 1 hour
• On-Demand
• Free Video

The Fundamental Theorem of Calculus: Point-Free Analysis

Explore point-free topology's innovative approach to calculus fundamentals through geometric logic, examining how spaces and continuity can be defined without traditional point-set methods.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

A Tour of EM(Cat#) in Category Theory

Delve into advanced category theory concepts, exploring monads in Cat#, morphisms, and Eilenberg-Moore objects through detailed mathematical examples and applications.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Monoidal Bicategories, Differential Linear Logic, and Analytic Functors

Delve into advanced mathematical concepts exploring bicategorical perspectives on linear logic, codereliction transformations, and the extension of Joyal's analytic functors in presheaf categories.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Effectful Trace Semantics via Effectful Streams

Explore effectful streams and their role in dataflow programming, focusing on trace semantics, cryptographic protocols, and bisimulation in Mealy machines.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Relations for Order Regular Categories

Explore advanced mathematical concepts in order regular categories and their relational structures through theoretical frameworks and practical applications.

• YouTube
• 1 hour
• On-Demand
• Free Video