Topos Institute Courses

Kleisli Constructions for Pseudomonads in Category Theory

Delve into advanced category theory concepts exploring Kleisli constructions, pseudomonads, and weighted limits in this mathematical deep-dive from the Topos Institute.

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

Amortized Analysis via Coalgebra

Explore coalgebraic perspectives on amortized analysis, examining how this mathematical framework enhances understanding of data structure operations and computational costs.

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

Engineering Practice and the Potential Role of Category Theory in Systems Engineering

Explore how information structures and categorical theory can enhance systems engineering processes, focusing on practical applications and standardized modeling approaches.

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

Collective Grassroots Knowledge Generation with Lab Discourse Graphs

Discover how discourse graphs revolutionize scientific research coordination by breaking down complex studies into interconnected questions, claims, and evidence for better knowledge synthesis and collaboration.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

What is it Like to be a Lax Double Functor? - Understanding Category Theory Models

Delve into advanced category theory concepts, exploring lax double functors, double theories, and their applications in CatColab, with insights into families of categories and presheaves.

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

Cartesian Polynomial Monads in Homotopy Type Theory

Explore how polynomial monads in homotopy type theory solve infinite coherence challenges in higher category theory, focusing on Finster, Allioux, and Sozeau's innovative approach.

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

Unraveling the Unreasonable Effectiveness of Mathematics in Natural Sciences

Explore the philosophical puzzle of mathematics' remarkable applicability to natural sciences, examining historical perspectives and challenging Wigner's "miracle" characterization through practical examples.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Graphical Methods in Quantum Cryptography - Visual Reasoning and Picture-Proofs

Explore visual reasoning techniques in quantum cryptography, focusing on picture-proofs and categorical quantum mechanics to simplify complex security protocol demonstrations.

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

Partial Markov Categories - Theory and Applications in Bayesian Inference

Delve into the algebraic foundations of Bayesian inference through string diagrams, exploring partial Markov categories and their applications in probability theory and decision-making problems.

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

Two Takeaways from Active Inference and Category Theory Workshop

Explore the intersection of category theory and active inference through key insights from the ACT2Infer workshop, including a polynomial functor perspective and workshop organization details.

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

Monad Translations Compose

Explore monad translations and their compositional properties through ML module systems, examining practical applications and theoretical foundations in functional programming.

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

Compact Proofs: Measuring Quality of Understanding with Compression-Based Metrics

Explore how compression-based metrics can evaluate and improve mechanistic interpretability in AI models, focusing on proof strategies and understanding model behavior.

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

Collaborative Modeling with Domain-Specific Categorical Logics - The Early Design of CatColab

Delve into the development of CatColab, a platform making category theory accessible for conceptual modeling across domains like programming, data science, and engineering through user-friendly categorical logics.

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

Safety by Shared Synthesis - AI-Enabled Formal Verification for Critical Infrastructure

Explore how AI-enabled formal verification tools can enhance cybersecurity and infrastructure safety through collaborative specification development and automated proof systems.

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

Stateful Lenses - A Recipe for Expressive Systems-Theoretic Cartesian Double Categories

Delve into advanced mathematical concepts of stateful lenses, exploring their role in systems theory through double categorical frameworks and their applications in resource sharing and Moore machines.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video