Lectures related to Natural Transformations in Algebra

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

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

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

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

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

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

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

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

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

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

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

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

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

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

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

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

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

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

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