In category theory, a branch of mathematics, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal twice yields the original category, so the opposite of an opposite category is the original category itself. In symbols, . (Wikipedia).
Are You Romantic or Classical?
The words 'Romantic' and 'Classical' usefully bring into focus important themes in our personalities. We're all both, but which are you a little more of? If you like our films take a look at our shop (we ship worldwide): http://www.theschooloflife.com/shop/all/ SUBSCRIBE to our channel for
From playlist RELATIONSHIPS
There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ
From playlist Philosophy of Science
Is There an Alternative to Political Correctness?
Political correctness aims for some very nice results, but its means have a habit of upsetting a lot of people. Might there be an alternative to it? We think there is, and it’s called Politeness. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/iVqWJ1 Joi
From playlist WORK + CAPITALISM
Linear versus Nonlinear Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Linear versus Nonlinear Differential Equations
From playlist Differential Equations
POP CULTURE: Better Celebrities
It’s easy to criticise modern societies for being ‘celebrity obsessed’. But the problem isn’t an interest in celebrity, it’s the sort of celebrities paraded before us. We don’t need no-celebrities, we need better-celebrities. Please subscribe here: http://tinyurl.com/o28mut7 If you like ou
From playlist POP CULTURE
Category Theory: The Beginner’s Introduction (Lesson 1 Video 4)
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. These videos will be discussed
From playlist Category Theory: The Beginner’s Introduction
How Is the ADHD Brain Different?
If you’re online, you may notice that conversations around ADHD are everywhere. You may even be starting to wonder, as you flick from one app to the next, that you yourself may have ADHD. So in Part 1 of this series about ADHD, Julian explores what this disorder is, what’s happening in the
From playlist Seeker+
Yinhuo Zhang: Braided autoequivalences, quantum commutative Galois objects and the Brauer groups
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 Algebra
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
Category Theory 1.3 : Properties and Types of Arrows
In this video, I introduce the opposite category, monics, epics, initial object, terminal objects, inverses, idempotent arrows, and more! Translate This Video : Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/fematika Email : fem
From playlist Category Theory
Ind and Pro Categories Associated to a Category
This is super basic. I ripped this off of ncatlab, one of the best websites on the planet.
From playlist Category Theory
Presheaves and Sheaves in Category Theory | Wrap it Up!
In this video, I will discuss presheaves and sheaves in the realm of category theory. This also discusses sites, covering families, and matching families. Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=ydS86qPbyJI Notes : None yet Patreon : https://www.patreon.c
From playlist Category Theory
Non-commutative motives - Maxim Kontsevich
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Maxim Kontsevich Institute for Advanced Study October 20, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a fo
From playlist Pierre Deligne 61st Birthday
Category Theory: The Beginner’s Introduction (Lesson 1 Video 5)
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. These videos will be discussed
From playlist Category Theory: The Beginner’s Introduction
Is It Better to Be Polite or Frank?
We live in an age that thinks highly of frankness and directness. But there are – nevertheless – a few reasons why politeness remains a hugely important quality. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/hMBQQs FURTHER READING “For most of hu
From playlist RELATIONSHIPS