Concept
Category (mathematics)
Related lectures (130)
Introduction to Model Categories
Explores lifting properties and model categories in topological spaces.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Categories and Functors
Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.
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.
Acyclic Models: Cup Product and Cohomology
Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.
Limits and colimits: Two examples
Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.
Introduction to Category Theory: Natural Transformations
Introduces natural transformations in category theory through concrete examples from group theory.
Introduction to Category Theory: Natural Transformations
Covers the concept of natural transformations between functors and their associativity.
Limits and colimits as adjoints: Chapter 1(c)
Explores the characterization of limits and colimits as adjoints in category theory.
Free Abelian Groups: Group Theory
Explores the concept of free abelian groups as an important left adjoint functor.