Lectures related to Equinumerosity

Category Theory: G-sets and Left Adjoint Functor

Explores the construction of G-sets and left adjoint functors in category theory.

Two Definitions of Group Action

Explores two definitions of group action on a set, focusing on properties and applications.

Linear Algebra: Injections, Surjections, Bijections

Explores injections, surjections, and bijections in linear algebra, highlighting their significance in mathematics.

Functions: Injections and Surjections

Explains injections, surjections, and bijections in functions with illustrative examples.

Group Actions on Sets

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.

Functions: Introduction and Terminology

Covers the introduction and terminology of functions, including injections, surjections, and bijections.

Motivations for studying group actions

Covers group actions, bijections, evaluations, translations, homomorphisms, and inverses within universal actions.

Motivations for Studying Actions: Universal Action of Bijections

Explores the motivations for studying actions through the universal action of bijections.

Sets and Functions

Introduces sets and functions, covering union, intersection, complement, functions terminology, and set operations analogies.

Linear Algebra: Surjections and Bijections

Explains surjections and bijections in linear algebra, focusing on function properties and inverse identification.

Introduction to Functions

Covers the basics of functions, including domain, codomain, image, and range, as well as injections, surjections, and bijections.

Linear Algebra: Bijections and Cardinality

Explores bijections in linear algebra and the concept of cardinality between sets.

Linear Algebra: Properties of Injective and Surjective Functions

Covers the properties of injective and surjective functions and the concept of bijections.

Function Composition

Covers the concept of function composition and the properties of bijections when composing functions.

Powers and Multiples: Subgroups and Stabilizers

Covers powers, multiples, subgroups, and stabilizers in group theory.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Group Theory: Torsion and Divisibility

Covers the concepts of torsion and divisibility in group theory.