Lectures related to Category Theory: Introduction

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

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

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

Introduces categories, concrete examples, opposite categories, and isomorphisms, leading to groupoids.

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

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

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

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

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

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

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

Introduces functors in category theory and explains their composition.

Introduces limits and colimits in a category, covering their properties and uniqueness.

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

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

Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.

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

Explores natural transformations in algebra, defining functors and isomorphisms.

Explores the concept of category theory, providing examples and discussing the opposite category concept.