Lectures related to Transfer of Model Structures

Simplicial and Cosimplicial Objects: Examples and Applications

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

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

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Adjunctions and Limits: Exploring Functors and Co-limits

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

Categories and Functors

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

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.

Homotopy theory of chain complexes

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

Limits and Colimits in Functor Categories

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

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and 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.

Categories and Functors: An Introduction

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

Category Theory: Introduction

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

Categories and Functors

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Functors and Adjunctions

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

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Construction of the homotopy category

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Active Learning in Category Theory

Explores examples of categories, morphisms, groupoids, and functors in category theory.

Natural Transformations Composition

Covers the theory of categories, emphasizing the importance of naturalness in the composition of transformations.

Derived functors: Identity and Homotopy Categories

Explores derived functors in model categories, focusing on identity and homotopy categories.