Lectures related to Categories and Functors

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

Category Theory: Introduction

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Categories and Functors

Explores building categories from graphs and the encoding of information by functors.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Active Learning in Category Theory

Explores examples of categories, morphisms, groupoids, and functors 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.

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

Natural Transformations: Functors and Categories

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Adjunctions: Constructing Desired Adjoints

Explores constructing desired adjoints in specific categories like Set.

Categories and Functors: An Introduction

Provides an overview of categories, functors, and natural transformations in mathematics.

Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.

Functors: Categories, Functors, and Natural Transformations

Introduces functors, including identity and forgetful functors, and explores duality functors.

Natural Transformations: Categories, Functors, and Equivalence

Covers natural transformations between functors, identity transformations, and equivalence of categories.

Natural Transformations: Examples and Applications

Explores natural transformations between functors in different categories and their applications.

Isomorphism in Categories

Covers the concept of isomorphism in categories, defining morphisms with inverses and exploring automorphisms and groupoids.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.