Topos Institute Courses

Developing Support for End-to-End Verification of Neural AI Agents

Explore Vehicle, a tool for writing, training, and formally verifying specifications for neural AI agents, with capabilities to export verified specifications to interactive theorem provers for environmental reasoning.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Combinatorial Foundation for Planar String Diagrams

Explore how diagrammatic sets provide a combinatorial foundation for 2D string diagrams, offering an alternative to Joyal and Street's topological approach with applications to (infty, n)-categories.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Duality for Complete Atomic Partial Boolean Algebras

Explore the mathematical duality theory for complete atomic partial Boolean algebras, focusing on quantum propositions and exclusivity graphs as an alternative to classical Stone-type duality in quantum logic contexts.

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

Composing Moore Machines - DOTS Lectures 4

Explore advanced mathematical frameworks for composing Moore machines using double operadic theory in systems modeling and categorical approaches.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

More Categories of Systems - DOTS Lectures 2

Explore advanced categorical structures in the Double Operadic Theory of Systems through David Jaz Myers' comprehensive mathematical framework.

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

Moore Machines - DOTS Lectures 3

Explore Moore machines within the Double Operadic Theory of Systems framework, examining state-based computational models and their mathematical foundations.

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

Categories of Moore Machines - DOTS Lectures 6

Explore the categorical structure of Moore machines within the Double Operadic Theory of Systems framework through advanced mathematical analysis.

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

Composing More Moore Machines - DOTS Lectures 5

Explore advanced composition techniques for Moore machines within the Double Operadic Theory of Systems framework with expert mathematical insights.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Symmetric Monoidal Double Categories of Systems - Lecture 7

Explore symmetric monoidal double categories and their applications to systems theory through advanced categorical structures and mathematical frameworks.

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

Opetopic Shapes, Combinatorially

Explore the combinatorial structures of opetopes through epiphytes, zoom complexes, and oriented face posets in this mathematical framework for higher-dimensional coherences.

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

Abstractions for Real People

Explore how mathematical abstractions in computing can better serve society through accessible, responsive approaches that address AI risks and societal needs.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Who Cares About Values? - Rethinking Human Values and Technology Through the Lens of Care

Explore the evolution of "human values" in technology design and discover how "care" offers a more nuanced framework for our relationship with technology than traditional value alignment.

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

ZX Calculus and Fault-Tolerant Quantum Computing

Explore ZX calculus applications in fault-tolerant quantum computing, covering error correction techniques and compositional approaches to quantum computation challenges.

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

2-Classifiers for 2-Algebras

Explore advanced category theory concepts through 2-classifiers for 2-algebras, examining discrete opfibration classifiers and their lifting properties in algebraic contexts.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Categories of Systems - DOTS Lectures 1

Explore the foundational concepts of system categories through David Jaz Myers' introduction to Double Operadic Theory of Systems (DOTS) mathematical framework.

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