Topos Institute Courses

Composing Instantaneous Machines - Theory and Implementation

Delve into the mathematical theory of instantaneous machines, exploring their composition, input-output dependencies, and the stabilization of systems through fixed-point analysis.

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

Categorical Approaches to Inferentialist Semantics

Explore the intersection of category theory and inferentialist semantics, examining structural relationships, open systems, and the unification of syntax and semantics in language philosophy.

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

Where is the Middle of a Fibonacci Sequence? - Finding the Center of Generalized Fibonacci Numbers

Explore the fascinating mathematical concept of locating the middle term in generalized Fibonacci sequences, leading to a natural organization system for these infinite number patterns.

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

Cubical Types for the Working Formalizer - Making Type Theory Accessible

Discover how to effectively use cubical type theory for formalizing mathematics, focusing on automation techniques that simplify complex theoretical concepts for practical applications.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Online Communities as Model Systems for Commons Governance

Explore how online communities serve as experimental grounds for self-governance, examining recruitment strategies, resource management, and institutional design across digital platforms.

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

What is the Identity Operator - Understanding Space, Time, and Memory

Explore the fundamental concept of identity morphisms across mathematics, physics, and Active Inference theory, examining its relationship with space, time, and memory.

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

Semantics for Reactive Probabilistic Programming

Delve into probabilistic synchronous languages and their semantics, exploring density-based interpretations, co-iterative execution, and relational frameworks for program equivalence verification.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

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