Topos Institute Courses

Introduction to Polynomial Functors - Lecture 1

Dive into polynomial functors, exploring distributive laws, universal properties, and fundamental concepts in category theory through expert-led mathematical discussions.

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

Polynomial Functors: Tensor Monoids and Internal Hom - Lecture 4

Delve into advanced mathematical concepts of polynomial functors, exploring tensor monoids, comonoids, and internal hom structures through comprehensive theoretical explanations.

• YouTube
• 2 hours 17 minutes
• On-Demand
• Free Video

Polynomial Functors and Comonoid Structures - Lecture 8

Delve into advanced mathematical concepts of polynomial functors, exploring comonoids, cofunctors, and bicomodules through detailed examples and theoretical constructions.

• YouTube
• 2 hours 25 minutes
• On-Demand
• Free Video

Polynomial Functors - Lecture 2

Delve into polynomial functors, exploring definitions, coalgebras, and compositions through advanced mathematical concepts and practical applications in category theory.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video

Polynomial Functors: Bicomodules - Lecture 9

Delve into advanced mathematical concepts of bicomodules and their applications in polynomial functors through expert-led theoretical exploration and analysis.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Polynomial Functors and State Machines - Lecture 6

Delve into polynomial functors, state machines, and ◁-monoids through advanced mathematical concepts and practical exercises in this theoretical mathematics exploration.

• YouTube
• 2 hours 13 minutes
• On-Demand
• Free Video

Polynomial Functors and Monoid Theory - Lecture 7

Delve into advanced mathematical concepts of polynomial functors, exploring ◁-monoids, their products, free structures, and comonoids through rigorous theoretical analysis.

• YouTube
• 2 hours 22 minutes
• On-Demand
• Free Video

Categories of Classes for Collection Monads - Algorithmic and Set Theory Perspectives

Delve into advanced category theory concepts exploring collection monads, their relation to Algebraic Set Theory, and applications in computational complexity through class-based models.

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

Diagrammatic Algebra of First Order Logic

Explore the neo-Peircean relations calculus and its diagrammatic representation of first-order logic, examining cartesian and linear bicategories in algebraic structures.

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

Co-Design of Complex Systems: From Autonomy to Future Mobility

Explore a framework for co-designing complex systems, focusing on future mobility solutions and autonomous vehicles through applied category theory and systemic optimization approaches.

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

Category Theory and Engineering Design - A Computational Support Challenge

Explore how category theory principles can enhance engineering design processes and computational support systems through advanced mathematical frameworks and practical applications.

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

Products in Double Categories Revisited

Delve into advanced mathematical concepts exploring products in double categories through a rigorous examination of theoretical foundations and practical applications in category theory.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Certainty or Intelligence - The Fundamental Incompatibility in Complex Systems

Explore the fundamental tension between mathematical certainty and artificial intelligence in complex systems, examining their compatibility in engineering and safety-critical applications.

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

Sociotechnical Infrastructure for Mathematics Research

Explore the intersection of technology, human collaboration, and mathematical research infrastructure through an analysis of cyberinfrastructure's role in advancing scientific discovery.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Semantic Foundations of Polarity Tagging

Explore the mathematical foundations of polarity tagging in natural language semantics, focusing on type hierarchies, preorders, and monotone functions in computational linguistics.

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