Topos Institute Courses

Algebraic Data Types and Self-Reference in Type Theory - From Theory to Version Control

Explore algebraic data types and their extension for self-referential structures, examining semantic interpretations through groupoids and mutation-based approaches for version control systems.

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

Polynomial Functors: From Elementary Arithmetic to Infinity-Operads

Explore polynomial functors and their applications in combinatorics, logic, and homotopy theory, from basic arithmetic concepts to complex infinity-operads.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Free Bicompletion of Categories Revisited - Part 1

Delve into advanced category theory concepts, exploring Whitman's theory extensions to free lattices, enriched categories, and applications in Linear Logic semantics.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

Cauchy Completeness and Adjoints in Double Categories

Delve into advanced category theory concepts, exploring Cauchy completeness, bimodules, and adjoints in double categories through examples from rings, rigs, and quantales.

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

Cohomological Aspects of Information

Explore the mathematical foundations of information cohomology, examining Shannon entropy, differential entropy, and categorical perspectives on information theory through a cohomological lens.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Aspects of a Mathematical Theory of Data - From Physical to Logical Specifications

Delve into mathematical theory of data specifications, exploring sketches of Range Categories, relational vs non-relational structures, and advanced normalization principles for logical data modeling.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video

The Functorial Difference Operator in Category Theory

Explore the mathematical concept of difference operators through Set theory and category theory, featuring combinatorial identities and practical examples for endofunctors.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Color Logic: A Visual Language for Dependent Categories

Explore a visual language system using colors, strings, and beads to understand dependent categories and category theory fundamentals through an innovative three-part framework.

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

Normalizing Ethical Reasoning in Mathematics - Teaching Resources and Responsible Development

Explore the integration of ethical considerations in mathematical work through practical tools and frameworks for identifying and addressing ethical implications in mathematical research and teaching.

• YouTube
• 1 hour 28 minutes
• Self-Paced
• Free Video

Higher Topos Theory and Goodwillie Calculus

Delve into advanced mathematical concepts exploring Lurie's higher topos theory, its relationship with Grothendieck's work, and connections to Goodwillie calculus through parametrized spectra and categorical structures.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Models for (∞,n)-Categories with Discreteness Conditions

Delve into advanced mathematical concepts exploring Segal spaces, (∞,n)-categories, and Θ_n-diagrams, examining discreteness conditions and completeness in category theory models.

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

Collaborative Editing via Category Theory

Explore the mathematical foundations of collaborative editing through category theory, examining operational transform algorithms and their connections to distributed systems and topology.

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

Higher Category Theory in Cat-Sharp

Delve into advanced categorical theory through polynomial comonads, exploring applications in database theory, effects handlers, and dynamical systems with focus on Cat^# structures.

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

Entropy and Diversity: The Axiomatic Approach

Explore the mathematical connections between ecological diversity, information entropy, and magnitude through an axiomatic lens, examining their applications across multiple scientific fields.

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

Computation in Continuous Dynamics

Explore the intersection of computation and continuous dynamics through advanced mathematical concepts and their applications in this theoretical mathematics seminar from Berkeley.

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