Functors: Assigning Morphisms and Dual Spaces

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Discusses the formulation of G-morphisms within vector spaces and topological spaces.

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

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

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

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

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

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

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