Higher category theory | Foundations of mathematics

Higher category theory

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).

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Category Theory 1.2: What is a category?

What is a Category?

From playlist Category Theory

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Category Theory 3.1: Examples of categories, orders, monoids

Examples of categories, orders, monoids.

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 9.1: Natural transformations

Natural transformations

From playlist Category Theory

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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

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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

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Category Theory 4.1: Terminal and initial objects

Terminal and initial objects

From playlist Category Theory

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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

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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

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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

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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

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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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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

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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

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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)

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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)

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Category Theory 2.1: Functions, epimorphisms

Functions, epimorphisms

From playlist Category Theory

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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

Related pages

Bicategory | Category of sets | Enriched category | Topological space | Homotopy | Quasi-category | Invariant (mathematics) | Topology | Category of small categories | Algebraic topology | Homotopy theory | Product (category theory) | Tricategory | Coherency (homotopy theory) | Hausdorff space | Path (topology) | Nonabelian algebraic topology | Mathematics | Cartesian product | Category theory | Categorification | Category (mathematics) | Morphism | Limit (category theory) | Functor | Fundamental groupoid | Higher-dimensional algebra | Monoidal category | Compactly generated space | Simplicial set