Category Theory Courses and Certifications

Topos Institute

Polynomial Functors and Dynamical Systems - Lecture 3

Delve into advanced concepts of polynomial functors, exploring dynamical systems composition, monoidal structures, and monoid theory in mathematical category theory.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Topos Institute

Polynomial Functors: Composition Product and Duoidality - Lecture 5

Delve into polynomial functors, exploring composition products, fundamental properties, and duoidality concepts through advanced mathematical theory and applications.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Topos Institute

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

Topos Institute

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

Topos Institute

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

Topos Institute

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

Topos Institute

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

Topos Institute

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

Topos Institute

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

Topos Institute

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

Topos Institute

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

Topos Institute

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
• On-Demand
• Free Video

Topos Institute

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
• On-Demand
• Free Video

Topos Institute

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
• On-Demand
• Free Video

Topos Institute

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
• On-Demand
• Free Video