Concept

Kernel (category theory)

Related lectures (31)

Group Actions: G-objects in a Concrete Category

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

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Groups and Homomorphisms

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

Quotients de groupe: Un cas particulier

Explores a categorical perspective on group quotients, focusing on a specific case.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Linear Applications: Kernel

Introduces the kernel of a linear application and its properties.

Hensel's Lemma Application

Discusses the application of Hensel's lemma in determining nth roots and elements that are nth powers.

Unitary Representations: Schur's Lemma

Explains Schur's Lemma on unitary representations and their irreducibility and invariance properties.

Variety Defined as the Closure of VCA

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Linear Algebra: Systems and Subspaces

Covers linear systems, vector subspaces, and the kernel and image of linear applications.

Applications of Lagrange's Theorem

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Information Measures: Part 2

Covers information measures like entropy, joint entropy, and mutual information in information theory and data processing.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Linear Applications in 3D: Rank Theorem

Explains the Rank Theorem for linear applications in 3D space and its implications.

Linear Algebra: Image and Kernel

Covers the concepts of image and kernel in linear algebra, focusing on uniqueness and orthogonal projections.

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Isomorphism Theorems: Quotients of Group

Explores the isomorphism theorems for quotient groups and the concept of surjective homomorphisms.

The inhomogeneous Ising chain

Covers the inhomogeneous Ising chain, Gibbs measures, and the Borel-Cantelli lemma.

Homomorphisms and Isomorphisms

Explores homomorphisms, isomorphisms, group properties, and their applications through examples and exercises.

Functors: Examples

Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.