Topos Institute Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Representable Behaviour in Double Categorical Systems Theory

Explore the application of category theory to systems study through Double Categorical Systems Theory, examining compositional structures, functorial behavior, and compositionality theorems.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Element Model Type Theory

Delve into a new implementation of generalized algebraic theories in Rust, exploring a type-theoretic approach that integrates e-graphs and enables theory composition for applications in scientific modeling and beyond.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

A Novel Modular and Compositional Framework for System Dynamics

Discover a novel framework for System Dynamics modeling based on Applied Category Theory, enhancing flexibility and applicability across domains, illustrated through COVID-19 modeling applications in Canadian jurisdictions.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Charles Peirce, Inference, and Category Theory

Explore how category theorists utilize Peirce's logical calculus, examining connections between his inference types (deduction, induction, abduction) and category-theoretic concepts of composition, extension, and lift.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

A Categorical Approach to Lyapunov Stability

Explore a categorical framework generalizing Lyapunov stability theory for dynamical systems, extending beyond classical applications to include metric spaces and quantale-enriched categories.

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