Lectures related to Closed monoidal category

Covers matrix equations as linear combinations, vector spaces, and geometric interpretations.

Introduces the theory of categories through examples and discusses the product of categories.

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

Explores the Hamilton-Jacobi equation in analytical mechanics, focusing on eigenvalues, constants of motion, and system predictability.

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

Covers examples of categories like sets, groups, and vector spaces, exploring composition and product formation.

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Explores Hamilton-Jacobi equations, phase portrait, and period calculation using action-angle variables for system trajectories.

Explains cofactors, eigenvectors, eigenvalues, and studying linear applications.

Explores equivalences, adjunctions, and simplicial enrichment in infinity category theory.

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

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Explores the characterization of fibrations and acyclic fibrations in chain complexes.

Explores the search for solutions in nonlinear systems through various methods and techniques.

Covers the concept of diagonalizability of matrices and explores eigenvalues and eigenvectors.

Covers the Gram-Schmidt algorithm for orthonormal bases in vector spaces.