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Subjects
Mathematics
Category Theory

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Explore the foundations of mathematics and abstract structures through category theory, including functors, higher categories, and their applications in science and software engineering. Learn from leading researchers via accessible YouTube lectures, ideal for beginners interested in mathematical logic and theoretical frameworks.

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Topos Institute
Applied Category Theory - MIT 2019

Explore mathematical structures and their real-world applications through category theory, covering foundational concepts to practical implementations in programming.
- YouTube
- 13 hours 25 minutes
- On-Demand
- Free Video
Topos Institute
A Tour of EM(Cat#) in Category Theory

Delve into advanced category theory concepts, exploring monads in Cat#, morphisms, and Eilenberg-Moore objects through detailed mathematical examples and applications.
- YouTube
- 1 hour 1 minute
- On-Demand
- Free Video
Topos Institute
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
- On-Demand
- Free Video
Topos Institute
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
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- Free Video
Topos Institute
Scientific and Software Engineering Applications of Category Theory

Explore how category theory enhances scientific programming by providing robust abstractions for data modeling, simulations, and workflows, leading to more maintainable and scalable solutions.
- YouTube
- 55 minutes
- On-Demand
- Free Video
Topos Institute
As If Category Theory Were a Foundation - A Methodological Approach to Mathematical Foundations

Explore the philosophical intersection of mathematics and methodology, examining how 'as-if' interpretations can bridge mathematical practice with theoretical foundations in category theory.
- YouTube
- 1 hour 20 minutes
- On-Demand
- Free Video
Topos Institute
Metric Spaces, Entropic Spaces and Convexity in Category Theory

Delve into advanced mathematical concepts exploring metric spaces, entropic spaces, and convexity monads, connecting thermodynamics with category theory and optimal transport.
- YouTube
- 59 minutes
- On-Demand
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Topos Institute
Philosophical Perspectives on Category Theory and Its Applications

Explore the philosophical implications of category theory across mathematics, physics, probability, and modern applications like machine learning and natural language processing.
- YouTube
- 1 hour 2 minutes
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- Free Video
GOTO Conferences
Basic Category Theory - An Introduction to Mathematical Foundations

Explore fundamental concepts of Category Theory through clear explanations of composition, morphisms, and functors, with practical applications in functional programming.
- YouTube
- 33 minutes
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- Free Video
ACM SIGPLAN
Univalent Double Categories - Formalization and Applications in Category Theory

Explore univalent double categories in category theory, their formalization in Coq, and applications in mathematics and computer science.
- YouTube
- 27 minutes
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Institute for Pure & Applied Mathematics (IPAM)
The Delannoy Category - Symmetric Tensor Categories and Representation Theory

Explore the Delannoy Category in symmetric tensor theory, featuring classification of simple objects, tensor product rules, and a combinatorial model using Delannoy paths.
- YouTube
- 52 minutes
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Institute for Pure & Applied Mathematics (IPAM)
The Spin Brauer Category - Extending Representation Theory

Explore the spin Brauer category, an extension of the Brauer category incorporating spin representation in orthogonal and symplectic group theory, presented by Alistair Savage at IPAM's workshop.
- YouTube
- 50 minutes
- On-Demand
- Free Video
Schmid College, Chapman University
Formalization of Infinity Category Theory

Explore ∞-category theory's formalization, unifying mathematics, computer science, and physics. Learn synthetic reasoning and the Yoneda Lemma in this advanced mathematical seminar.
- YouTube
- 1 hour 51 minutes
- On-Demand
- Free Video
Topos Institute
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
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Topos Institute
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.
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