Equivalence (mathematics) | Algebraic geometry

In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined intersection products. Pierre Samuel formalized the concept of an adequate equivalence relation in 1958. Since then it has become central to theory of motives. For every adequate equivalence relation, one may define the category of pure motives with respect to that relation. Possible (and useful) adequate equivalence relations include rational, algebraic, homological and numerical equivalence. They are called "adequate" because dividing out by the equivalence relation is functorial, i.e. push-forward (with change of codimension) and pull-back of cycles is well-defined. Codimension 1 cycles modulo rational equivalence form the classical group of divisors modulo linear equivalence. All cycles modulo rational equivalence form the Chow ring. (Wikipedia).

Put all three properties of binary relations together and you have an equivalence relation.

From playlist Abstract algebra

Set Theory (Part 6): Equivalence Relations and Classes

Please feel free to leave comments/questions on the video and practice problems below! In this video, I set up equivalence relations and the canonical mapping. The idea of equivalence relation will return when we construct higher-level number systems, e.g.integers, from the natural number

From playlist Set Theory by Mathoma

Equivalence Relations Definition and Examples

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.

From playlist Abstract Algebra

This video is a full introduction to equivalence relations. Timestamps: 0:00 What is a relation? 3:02 Terminology - A Relation defined on a Set 4:02 Equivalence Relation Definition 7:18 Reflexive 9:18 Symmetric 11:48 Transitive Thanks for watching! Comment below with questions, and make

From playlist Proofs

Univalent foundations and the equivalence principle - Benedikt Ahrens

Short Talks by Postdoctoral Members Benedikt Ahrens - September 21, 2015 http://www.math.ias.edu/calendar/event/88134/1442858400/1442859300 More videos on http://video.ias.edu

From playlist Short Talks by Postdoctoral Members

The picture in the lecture was taken from Wikipedia: https://en.wikipedia.org/wiki/Demographics_of_the_United_States#/media/File:USA2020dec1.png

From playlist Abstract Algebra 1

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Exploring a special kind of relation, called an equivalence relation. Equivalence classes and partitions are also discussed. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

From playlist Discrete Math I (Entire Course)

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From playlist The New CHALKboard

Introduction to Theory of Literature (ENGL 300) In this lecture on the work of Roman Jakobson, Professor Paul Fry continues his discussion of synchrony and diachrony. The relationships among formalism, semiotics, and linguistics are explored. Claude Levi-Strauss's structural interpretat

From playlist Introduction to Theory of Literature with Paul H. Fry

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From playlist Engineering

Equivalences and Partitions, Axiomatic Set Theory 2 2

Defining equivalences and partitions of sets, and proving some theorems about their relations to each other. My Twitter: https://twitter.com/KristapsBalodi3 Equivalence Relations:(0:00) Partitions:(9:22) Connecting Equivalence and Partitions:(14:09) Representatives:(27:04)

From playlist Axiomatic Set Theory

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From playlist Palamas and Thomism

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From playlist Mathematics

Two Equivalence Classes [a] and [b] Are Equal If and Only If a is Related to b

In this video I prove a statement surrounding relations. We have an equivalence relation on a set A and we have to show that the equivalence class of a is equal to the equivalence class of b if and only if a is related to b. If you enjoyed this video please consider liking, sharing, and

From playlist Relations

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From playlist Mathematics

Important Math Proof: The Set of Equivalence Classes Partition a Set

In this video I prove a very important result in mathematics. Given an equivalence relation R on a nonempty set A, the set S of equivalence classes of A is a partition of A. Stated another way, this result says we can write A as a disjoint union of equivalence classes. The pencils I used

From playlist Relations

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From playlist Linux Essentials For Hackers