Topos Institute Courses

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

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

How Rust Won - The Quest for Performant, Reliable Software

Discover how Rust revolutionized programming by solving the tension between performance and memory safety through innovative language design and community building.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Towards a Mathematical Theory of Intentional Systems

Explore mathematical frameworks for understanding beliefs, goals, and actions in systems through Dennett's intentional stance, Bayesian approaches, and categorical systems theory.

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

A Characterization of Pro-representable Virtual Double Categories

Explore pro-representable virtual double categories and their role in formal category theory, including exponentiable structures and internal-hom candidates.

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

Composing "Flavoured" Petri nets

Explore the double operadic theory of systems framework to understand how various flavors of Petri nets can be composed and analyzed through mathematical doctrine.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Dependetopes and Higher Generalized Algebraic Theories

Explore dependetopes as a syntactic approach to higher generalized algebraic theories, bridging categorical algebra and type theory through dependent typing extensions.

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

Behavioural Modules of Systems - DOTS Lectures 9

Explore advanced categorical systems theory through behavioral modules, examining how systems interact and compose using double operadic frameworks.

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

Compositionality of Flavoured Petri Nets

Explore the natural nesting composition of flavoured Petri nets with extra data from symmetric monoidal double categories and their intended semantics.

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

Double Categorical Equivalences

Explore double categories and their equivalences using homotopy theory to identify canonical gregarious equivalences, revealing multiple model structures for 2-dimensional categorical frameworks.

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

Applying the Representability Theorem - Examples of Compositional Behaviours - Lecture 14

Explore compositional behaviors through the representability theorem in categorical systems theory with practical examples from the Double Operadic Theory of Systems framework.

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

A Taste of Quantitative Logic

Explore quantitative logic where judgments are valued in real numbers, featuring sequent calculus for quantitative linear logic with applications in machine learning.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Concrete Syntax Matters, Actually

Explore how concrete syntax shapes programmer interaction with languages, examining asynchronous control flow, gradual subtyping, and first-class functions through usability lens.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video