Lectures related to Functor represented by a scheme

Explores G-objects in a concrete category and the framework for group actions.

Introduces the concept of restriction functors in group actions.

Discusses the properties of products in categories and their relationship with small and arbitrary categories.

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Explores natural transformations in category theory with a focus on the functor L and its algebraic properties.

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

Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Explores the construction and properties of the free abelian group FAb(X) and its categorical extensions.

Explores the association of Lie algebras to algebraic groups and homomorphisms.

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

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

Explores the restriction functor in group theory, focusing on its properties.

Explores the Hom functor for abelian groups and its relation to direct sums.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores Lie groups, scalar fields, and vector spaces transformations.

Covers limits, colimits, standard simplices, mapping spaces, boundaries, horns, and spines.

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

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

Explores the dynamics of a block pulled by a spring under various conditions.