Higher category theory | Foundations of mathematics
In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher category theory is often applied in algebraic topology (especially in homotopy theory), where one studies algebraic invariants of spaces, such as their fundamental weak ∞-groupoid. (Wikipedia).
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
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
Higher Dimensional Syntax - Eric Finster
Eric Finster Ecole Polytechnique Federal de Lausanne; Member, School of Mathematics September 27, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Recommended books for the undergrad category theorist
I'll talk more about universal constructions on this channel, so best subscribe. In this video I go through a curated list of introductory text about category theory. You can find the list here: https://gist.github.com/Nikolaj-K/282515e58c1c14de2e25222065f77a0a In the video I comment on a
From playlist Algebra
Category Theory 4.1: Terminal and initial objects
Terminal and initial objects
From playlist Category Theory
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
Charles Rezk - 1/4 Higher Topos Theory
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/RezkNotesToposesOnlinePart1.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
27 Unhelpful Facts About Category Theory
Category theory is the heart of mathematical structure. In this video, I will drive a stake through that heart. I don't know why I made this. Grothendieck Googling: https://mobile.twitter.com/grothendieckg Join my Discord server to discuss this video and more: https://discord.gg/AVcU9w5g
From playlist Mathematics
Benedikt Ahrens - Univalent Foundations and the UniMath library - IPAM at UCLA
Recorded 13 February 2023. Benedikt Ahrens of Delft University of Technology presents "Univalent Foundations and the UniMath library" at IPAM's Machine Assisted Proofs Workshop. Abstract: Univalent Foundations (UF) were designed by Voevodsky as a foundation of mathematics that is "invarian
From playlist 2023 Machine Assisted Proofs Workshop
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
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
Constructive Type Theory and Homotopy - Steve Awodey
Steve Awodey Institute for Advanced Study December 3, 2010 In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in
From playlist Mathematics
Duality in Higher Categories-I by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Jens Eberhardt: Motivic Springer Theory
27 September 2021 Abstract: Algebras and their representations can often be constructed geometrically in terms of convolution of cycles. For example, the Springer correspondence describes how irreducible representations of a Weyl group can be realised in terms of a convolution action on
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Symmetries in QFT and their Relationship with Category Theory (Lecture 3) by Lakshya Bhardwaj
INFOSYS-ICTS STRING THEORY LECTURES SYMMETRIES IN QFT AND THEIR RELATIONSHIP WITH CATEGORY THEORY SPEAKER: Lakshya Bhardwaj (Mathematical Institute, University of Oxford) DATE : 10 October 2022 to 12 October 2022 VENUE: Madhava Lecture Hall (Hybrid) Lecture 1: 10 October 2022 at 3:30 pm
From playlist Infosys-ICTS String Theory Lectures