In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category. This idea often allows restating of definitions or properties of morphisms (such as monomorphism or product) given by a universal property in more familiar terms, by stating their relation to elements. Some very general theorems, such as Yoneda's lemma and the Mitchell embedding theorem, are of great utility for this, by allowing one to work in a context where these translations are valid. This approach to category theory – in particular the use of the Yoneda lemma in this way – is due to Grothendieck, and is often called the method of the functor of points. (Wikipedia).
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
Intuitive Introduction to Category Theory
Category Theory offers a different style of thinking about mathematics. I describe how using functions and sets as examples. Join our Discord to engage with other Mathematics enthusiasts ! https://discord.gg/yyDzhKXUBV Patreon: https://www.patreon.com/MetaMaths Source code for animatio
From playlist Category Theory course
AMMI 2022 Course "Geometric Deep Learning" - Lecture 11 (Beyond Groups) - Petar Veličković
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 11: Category Theory • Set category • Functors • Natural
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
On Voevodsky's univalence principle - André Joyal
Vladimir Voevodsky Memorial Conference Topic: On Voevodsky's univalence principle Speaker: André Joyal Affiliation: Université du Québec á Montréal Date: September 11, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Towards elementary infinity-toposes - Michael Shulman
Vladimir Voevodsky Memorial Conference Topic: Towards elementary infinity-toposes Speaker: Michael Shulman Affiliation: University of San Diego Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
On the Setoid Model of Type Theory - Erik Palmgren
Erik Palmgren University of Stockholm October 18, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
This lecture is part of an online course on Category theory This is the introductory lecture, where we give a few examples of categories and define them. The lectures were originally part of a graduate algebra course, and give a quick overview of the basic category theory that is useful
From playlist Categories for the idle mathematician
The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories - Emily Riehl
Vladimir Voevodsky Memorial Conference Topic: The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories Speaker: Emily Riehl Affiliation: Johns Hopkins University Date: September 12, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Jules Hedges - compositional game theory - part I
Compositional game theory is an approach to game theory that is designed to have better mathematical (loosely “algebraic” and “geometric”) properties, while also being intended as a practical setting for microeconomic modelling. It gives a graphical representation of games in which the flo
From playlist compositional game theory
A Sensible Introduction to Category Theory
Remember when I used a video with a coconut in the thumbnail to drive a stake through the heart of mathematical structure? Today, in this introduction to the basics of category theory, I attempt to remove it. 27 Unhelpful Facts About Category Theory: https://www.youtube.com/watch?v=H0Ek86
From playlist Mathematics
Category Theory 1.1: Motivation and Philosophy
Motivation and philosophy
From playlist Category Theory