Topos Institute Courses

Does It Matter Whether There Are Infinite Sets?

Explore the philosophical and mathematical foundations of set theory, examining the axiom of infinity and its implications for modern mathematics, programming, and handling "big" objects.

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

Classical and Constructive Logics Together: Ecumenical Systems

Explore Ecumenical Logic systems that combine classical and intuitionistic logic, examining their proof theoretical properties and potential for enhancing interoperability between proof assistants.

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

Instances of Models of Double-Categorical Theories

Explore instances of models in double-categorical theories through Kevin Carlson's recent research, uncovering their significance and applications in category theory.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

A General Representability Theorem for Systems Theory - Part 3

Explore advanced categorical systems theory through David Jaz Myers' third lecture on general representability theorems in the Double Operadic Theory of Systems framework.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Distillation Systems as Models of Homotopy Colimits

Delve into the mathematical concept of distillation systems and their relationship to homotopy colimits in category theory, exploring how these structures govern properties needed for functor calculus.

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

AI for Precision Oncology

Discover how artificial intelligence revolutionizes personalized cancer treatment through precision oncology approaches and cutting-edge computational methods.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Cartesian Fermat Categories - A New Class of Cartesian Differential Categories

Explore Cartesian Fermat categories as a new framework bridging differential calculus and category theory, with applications to machine learning and automatic differentiation.

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

Update Rules of Pearl and Jeffrey in Probabilistic Updating

Explore the differences between Pearl and Jeffrey's probabilistic updating rules, their applications in multiple data scenarios, and their role in machine learning algorithms like Expectation Maximization.

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

The Path-Complete Formalism for Switched Systems: Stability and Beyond

Explore the path-complete Lyapunov framework for analyzing switched systems, covering stability analysis, constrained switching, stabilization techniques, and safety through barrier functions.

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

V-graded Categories for Enrichment and Actions of Monoidal Categories

Explore V-graded categories as a unifying framework for enriched categories and V-actegories, understanding how they accommodate arbitrary monoidal categories through parameterized morphisms.

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

Articulating the Structure of Reasons

Explore how semantic inferentialism understands propositional content through reason relations, examining both proof-theoretic and model-theoretic approaches to substructural logic.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Double Functorial Representation of Indexed Monoidal Structures

Explore double category theory's role in capturing substitution and quantification operations in logical doctrines through spans and quintets.

• YouTube
• 1 hour 7 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

Incremental Homomorphism Search

Explore incremental search problems and how they efficiently update query results when underlying data changes, with applications in relational databases and category theory.

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