What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
Abstract Algebra | Injective Functions
We give the definition of an injective function, an outline of proving that a given function is injective, and a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
The Composition of Injective(one-to-one) Functions is Injective Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the composition of injective(one-to-one) functions is also injective(one-to-one)
From playlist Proofs
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
Schemes 42: Very ample sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define ample and very ample invertible sheaves for projective varieties, and gives some examples for complex elliptic curves. We also show that some sect
From playlist Algebraic geometry II: Schemes
The Definition of an Injective(One to One) Function and Explanation
The Definition of an Injective(One to One) Function and Explanation
From playlist Functions, Sets, and Relations
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
Who Gives a Sheaf? Part 1: A First Example
We take a first look at (pre-)sheaves, as being inspired from first year calculus.
From playlist Who Gives a Sheaf?
How to Prove a Function is Injective(one-to-one) Using the Definition
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to prove a function is injective. Injective functions are also called one-to-one functions. This is a short video focusing on the proof.
From playlist Proofs
Schemes 3: exactness and sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In it we discuss exactness of morphisms of sheaves over a topological space.
From playlist Algebraic geometry II: Schemes
Čech cohomology part II, Čech-to-derived spectral sequence, Mayer-Vietoris, étale cohomology of quasi-coherent sheaves, the Artin-Schreier exact sequence and the étale cohomology of F_p in characteristic p.
From playlist Étale cohomology and the Weil conjectures
From Cohomology to Derived Functors by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. Given a continuous map between topological spaces there are two natural ways to transfer sheaves from one space to another. We summarize the main properties of
From playlist Algebraic geometry II: Schemes
Grothendieck-Serre Duality by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Schemes 27: Quasicoherent sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We show how to turn a module over a ring into a sheaf of modules over its spectrum. A quasicoherent sheaf of modules of one which looks locally like one constr
From playlist Algebraic geometry II: Schemes
Charles Weibel: K-theory of line bundles and smooth varieties
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. We give a K-theoretic criterion for a quasi-projective variety to be smooth, generalizing the proof of Vorst's conjecture for affine varieties. If L is a line bundle corresponding to
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Leray spectral sequence continued, computing derived pushforwards, strict henselizations and stalks of derived pushforwards, Weil-Divisor exact sequence, cohomology of the sheaf of divisors, reduction to Galois cohomology, intro to Brauer groups
From playlist Étale cohomology and the Weil conjectures
Schemes 45: Blowing up schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we discuss the operation of blowing up a scheme along a sheaf of ideals. This can be used to make ideals invertible, and to eliminate points o
From playlist Algebraic geometry II: Schemes
Schemes 34: Coherent sheaves on projective space
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. This lecture discusses some of Serre's theorems about coherent sheaves on projective space. In particular we describe how coherent sheaves are related to finit
From playlist Algebraic geometry II: Schemes
Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one). Given two functions f : A to B and g: B to C, we prove that if the composition g o f: A to C is an injective function then f is also an injective function
From playlist Proofs