Category theory

Generator (category theory)

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).

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Category Theory 2.1: Functions, epimorphisms

Functions, epimorphisms

From playlist Category Theory

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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

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Category Theory 1.2: What is a category?

What is a Category?

From playlist Category Theory

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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

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Category Theory 1.1: Motivation and Philosophy

Motivation and philosophy

From playlist Category Theory

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Category Theory 9.1: Natural transformations

Natural transformations

From playlist Category Theory

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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

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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

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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

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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

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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)

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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

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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

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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

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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)

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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

Related pages

Category of sets | Mathematics | Set (mathematics) | Annihilator (ring theory) | Categories for the Working Mathematician | Dual (category theory) | Ring (mathematics) | Category theory | Grothendieck category | Category (mathematics) | Morphism