Monoidal categories | Binary relations
In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism (or arrow) R : A → B in this category is a relation between the sets A and B, so R ⊆ A × B. The composition of two relations R: A → B and S: B → C is given by (a, c) ∈ S o R ⇔ for some b ∈ B, (a, b) ∈ R and (b, c) ∈ S. Rel has also been called the "category of correspondences of sets". (Wikipedia).
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
Working with Functions (1 of 2: Notation & Terminology)
More resources available at www.misterwootube.com
From playlist Working with Functions
Introduction to Relations and Functions (L9.1)
This lesson introduces functions and explains how to determine if a relations is a function. The vertical line also used. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Introduction to Functions: Function Basics
10 Relations (still with the not-so-exciting-stuff)
This video introduces relations between pairs of elements.
From playlist Abstract algebra
Intro to Real Functions (3 of 4: Characteristics of a function)
More resources available at www.misterwootube.com
From playlist Working with Functions
Put all three properties of binary relations together and you have an equivalence relation.
From playlist Abstract algebra
Introduction to Relations and Functions
An introduction to relations and functions. Discussion includes defining, classifying, and examples of relations and functions, as well as five ways to represent relations and functions,
From playlist Algebra 1
Determine if a Relation is a Function
http://mathispower4u.wordpress.com/
From playlist Intro to Functions
Introduction to Functions (1 of 2: Basic Idea & Formal Definition)
More resources available at www.misterwootube.com
From playlist Working with Functions
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
Juliet Cooke: Skein categories
In this talk we will talk about skein categories which are a categorical analogue of skein algebras based on coloured ribbon tangles. We shall then see how these skein categories satisfy excision and therefore fit within the framework of factorisation homology as k-linear factorisation hom
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Winter School JTP: From Hall algebras to legendrian skein algebras, Fabian Haiden
A mysterious relation between Hall algebras of Fukaya categories of surfaces and skein algebras was suggested by recent work of Morton-Samuelson and Samuelson-Cooper. I will discuss how this relation can be made precise using knot theory of legendrian curves and general gluing properties o
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
The Heisenberg Algebra in Symplectic Algebraic Geometry - Anthony Licata
Anthony Licata Institute for Advanced Study; Member, School of Mathematics April 2, 2012 Part of geometric representation theory involves constructing representations of algebras on the cohomology of algebraic varieties. A great example of such a construction is the work of Nakajima and Gr
From playlist Mathematics
Yann Palu, Research talk - 2 February 2015
Yann Palu (Université de Picardie) - Research talk http://www.crm.sns.it/course/4456/ Motivated by the theory of cluster algebras, Buan-MarshReiten proved that some quotients of cluster categories are module categories. More generally, some subquotients (associated with rigid objects) of
From playlist Lie Theory and Representation Theory - 2015
Representation Theory & Categorification II - Catharina Stroppel
2021 Women and Mathematics - Uhlenbeck Course Lecture Topic: Representation Theory & Categorification II Speaker: Catharina Stroppel Affiliation: University of Bonn Date: May 25, 2021 In modern representation theory we often study the category of modules over an algebra, in particular i
From playlist Mathematics
Séminaire Bourbaki 08/11/2014 - Aurélien Djament 2/4
" La propriété noethérienne pour les foncteurs entre espaces vectoriels " [d'après A. Putman, S. Sam et A. Snowden] Les bases de Gröbner permettent de démontrer le théorème de la base de Hilbert, en ramenant le caractère noethérien à une propriété combinatoire d'ensembles ordonnés. A. P
From playlist Bourbaki - 08 novembre 2014
The affine Hecke category is a monoidal colimit - James Tao
Geometric and Modular Representation Theory Seminar Topic: The affine Hecke category is a monoidal colimit Speaker: James Tao Affiliation: Massachusetts Institute of Technology Date: February 24, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
Lecture 12: Classifying topoi (Part 1)
This is the first of several talks on the subject of classifying topoi. I began with a brief reminder of the overall picture from the first talk, i.e. what are classifying topoi and why do we care (from the point of view of organising mathematics). Then I spent some time talking about tens
From playlist Topos theory seminar
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 15
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence