In mathematics, specifically category theory, a family of generators (or family of separators) of a category is a collection of objects in , such that for any two distinct morphisms in , that is with , there is some in and some morphism such that If the collection consists of a single object , we say it is a generator (or separator). Generators are central to the definition of Grothendieck categories. The dual concept is called a cogenerator or coseparator. (Wikipedia).
Category Theory: The Beginner’s Introduction (Lesson 1 Video 2)
Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. Follow me on Twitter: @mjmcodr
From playlist Category Theory: The Beginner’s Introduction
PNWS 2014 - What every (Scala) programmer should know about category theory
By, Gabriel Claramunt Aren't you tired of just nodding along when your friends starts talking about morphisms? Do you feel left out when your coworkers discuss a coproduct endofunctor? From the dark corners of mathematics to a programming language near you, category theory offers a compac
From playlist PNWS 2014
Category theory for JavaScript programmers #19: some formality around categories
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Category Theory 1.1: Motivation and Philosophy
Motivation and philosophy
From playlist Category Theory
Category theory for JavaScript programmers #27: string diagrams
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Yonatan Harpaz - New perspectives in hermitian K-theory I
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Huawei Young Talents Programme - Laurent Lafforgue
The online ceremony celebrating the official launch of the Huawei Young Talents Program at the Institut des Hautes Etudes Scientifiques was held on 6 November 2020. This program aims to support the work of talented researchers in mathematics and theoretical physics at the beginning of thei
From playlist Huawei Young Talents Program - November 2020
Laurent Lafforgue - 1/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Tudor Dimofte - 3d SUSY Gauge Theory and Quantum Groups at Roots of Unity
Topological twists of 3d N=4 gauge theories naturally give rise to non-semisimple 3d TQFT's. In mathematics, prototypical examples of the latter were constructed in the 90's (by Lyubashenko and others) from representation categories of small quantum groups at roots of unity; they were rece
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Anna Marie Bohmann: Assembly in the Algebraic K-theory of Lawvere Theories
Talk by Anna Marie Bohmann in Global Noncommutative Geometry Seminar (Americas), https://globalncgseminar.org/talks/tba-30/, on April 29, 2022.
From playlist Global Noncommutative Geometry Seminar (Americas)
David Ben-Zvi: Geometric Langlands correspondence and topological field theory - Part 1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Laurent Lafforgue - 4/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Laurent Lafforgue - 3/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Ulrich Bunke: Coarse homotopy theory and K-theory
Talke by Ulrich Bundle in Global Noncommutative Geometry Seminar (Americas) on September 30, 2022. https://globalncgseminar.org/talks/tba-36/
From playlist Global Noncommutative Geometry Seminar (Americas)
Inernal Languages for Higher Toposes - Michael Shulman
Michael Shulman University of California, San Diego; Member, School of Mathematics October 3, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics