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Lecture
Category Theory: Natural Transformations and Adjunctions
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Category Theory: Introduction
Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.
Homotopical Algebra: Introduction
Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.
Limits and Colimits in Functor Categories
Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.
Adjunctions and Functor Categories: Exploring Connections
Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.
Natural Transformations
Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.
Quasi-Categories: Active Learning Session
Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.
Limits and colimits as adjoints: Chapter 1(c)
Explores the characterization of limits and colimits as adjoints in category theory.
Natural Transformations: Examples and Applications
Explores natural transformations between functors in different categories and their applications.
Model Categories and Homotopy Theory: Functorial Connections
Covers the relationship between model categories and homotopy categories through functors preserving structural properties.
Limits and colimits: Introduction, Chapter 1(c)
Introduces limits and colimits in a category, covering their properties and uniqueness.
