Topos Institute Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

AI-Assisted Coding - Correct by Construction Not by Generation

Explore how AI can assist in constructing provably correct code through systematic approaches rather than relying on pure code generation techniques.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Network Mathematics for All

Explore network mathematics fundamentals and their real-world applications through an accessible introduction to graph theory, connectivity patterns, and mathematical modeling concepts.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Canonical Extensions of Quantale Enriched Categories

Explore advanced mathematical concepts in quantale enriched categories and their canonical extensions through rigorous theoretical analysis and practical applications.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

An Introduction to Superoscillations and Supershift

Explore the fascinating mathematical concept of superoscillations and supershift through an advanced theoretical analysis of their properties, applications, and fundamental principles.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Domain-specific Logics for Scientific Modeling - Theory and Practice

Explore domain-specific logics for scientific modeling through theoretical foundations and practical applications, emphasizing innovative approaches to mathematical reasoning and model development.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Probabilistic and Namespace Conditioning in Polynomial Functors

Delve into probabilistic conditioning and namespace theory through polynomial functors, exploring Bayesian inference and distributive maps in substitution monoidal products.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Polynomial Functors and Dynamical Systems - Lecture 3

Delve into advanced concepts of polynomial functors, exploring dynamical systems composition, monoidal structures, and monoid theory in mathematical category theory.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Polynomial Functors: Composition Product and Duoidality - Lecture 5

Delve into polynomial functors, exploring composition products, fundamental properties, and duoidality concepts through advanced mathematical theory and applications.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video