Category theory | Simplicial sets
In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C. These closely related objects can provide information about some familiar and useful categories using algebraic topology, most often homotopy theory. (Wikipedia).
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
Category Theory 1.1: Motivation and Philosophy
Motivation and philosophy
From playlist Category Theory
Category theory for JavaScript programmers #19: some formality around categories
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Category Theory 4.1: Terminal and initial objects
Terminal and initial objects
From playlist Category Theory
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
Introduction To Complete Segal Spaces by Rekha Santhanam
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)
Ieke Moerdijk: An Introduction to Dendroidal Topology
Talk by Ieke Moerdijk in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/an-introduction-to-dendroidal-topology/ on April 23, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Homotopy Category As a Localization by Rekha Santhanam
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)
Higher Algebra 1: ∞-Categories
In this video, we introduce ∞-categories. This is the first of a series of videos towards a reasonably non-technical overview over stable ∞-categories and Higher Algebra, which are intended to be watchable independently from the main lecture. Further resources: M.Boardman and R.Vogt. Homo
From playlist Higher Algebra
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 4
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Stable Homotopy Seminar, 14: The stable infinity-category of spectra
I give a brief introduction to infinity-categories, including their models as simplicially enriched categories and as quasi-categories, and some categorical constructions that also make sense for infinity-categories. I then describe what it means for an infinity-category to be stable and h
From playlist Stable Homotopy Seminar
Perverse schobers and semi-orthogonal decompositions - Mikhail Kapranov
Vladimir Voevodsky Memorial Conference Topic: Perverse schobers and semi-orthogonal decompositions Speaker: Mikhail Kapranov Affiliation: Institute for Advanced Study Date: September 14, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Inna Zakharevich : Coinvariants, assembler K-theory, and scissors congruence
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
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
Christoph Winges: On the isomorphism conjecture for Waldhausen's algebraic K-theory of spaces
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I will survey recent progress on the isomorphism conjecture for Waldhausen's "algebraic K-theory of spaces" functor, and how this relates to the original isomorp
From playlist HIM Lectures: Junior Trimester Program "Topology"