Lectures related to Natural transformation

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Functors and Adjunctions

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

Natural Transformations: Categories, Functors, and Equivalence

Covers natural transformations between functors, identity transformations, and equivalence of categories.

The Topological Künneth Theorem

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Natural Transformations: Examples and Applications

Explores natural transformations between functors in different categories and their applications.

Introduction to Category Theory: Natural Transformations

Covers the concept of natural transformations between functors and their associativity.

Introduction to Group Theory: Motivation

Introduces adjunctions in Group Theory with examples of natural transformations and isomorphisms.

Natural Transformations and Functors

Covers natural transformations, functors, and their composition properties in category theory.

Natural Transformations: Functors and Categories

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

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Equivalence: Natural Isomorphisms and Triangular Identities

Covers the existence of natural isomorphisms and transformations with triangular identities.

Introduction to Category Theory: Adjoint Functors

Introduces the concept of adjoint functors in category theory, focusing on the characterization of adjunctions.

Adjunctions and Functor Categories: Exploring Connections

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

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Category Equivalence

Explores the concept of category equivalence through isomorphic functors and natural isomorphisms between categories.

Equivalences of Categories

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Natural Transformations: Epsilon Transformation

Explores the epsilon transformation in group theory and category theory, emphasizing linearity and naturality.

Homotopical Algebra

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

Functors and Natural Transformations

Delves into functors, natural transformations, and group actions with explicit examples.

Homotopical Algebra: (Co)Limits

Explores the concept of (co)limits in homotopical algebra, discussing functor relations, special cases, and the universal properties of colimits and limits.