Lecture 1 - Introduction to Category Theory
Lecture 2 - Examples of Categories
Lecture 3 - Functors
Lecture 4 - Natural Transformations and Equivalences of Categories
Lecture 5 - Equivalence of Categories and some properties of morphisms
Lecture 6 - The Yoneda lemma and Representable functors
Lecture 7 - Limits and colimits - Part 1
Lecture 8 - Limits and colimits - Part 2
Lecture 9 - Limits and colimits - Part 3 - Interaction with functors - Adjuctions - I Definitions
Lecture 10 - Adjunctions - II Examples
Lecture 11 - Adjunctions - III Triangular identities
Lecture 12 - Adjunctions - IV General adjoint functor theorem
Lecture 13 - Adjunctions - V Special adjoint functor theorem Filtered colimits-I Basics
Lecture 14 - Filtered colimits - II Locally finitely presentable (LFP) categories
Lecture 15 - Monads - I Eilenberg-Moore and Kleisli categories
Lecture 16 - Monads - II Monadicity theorem
Lecture 17 - Monoidal categories and enriched categories
Lecture 18 - Abelian categories
Lecture 19 - Grothendieck categories and localization
Lecture 20 - Freyd-Mitchell embedding theorem Homological algebra I Diagram chasing
Lecture 21 - Homological algebra II Chain homotopy, projective resolutions and the derived category
Lecture 22 - Model categories
Lecture 23 - Topos Theory - I Elementary toposes
Lecture 24 - Topos Theory - II Grothendieck toposes
