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
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
(0.3.101) Exercise 0.3.101: Classifying Differential Equations
This video explains how to classify differential equations based upon their properties https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
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
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: 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
K-Motives and Koszul Duality in Geometric Representation Theory - Jens Eberhardt
K-Motives and Koszul Duality in Geometric Representation Theory - Jens Eberhardt Geometric and Modular Representation Theory Seminar Topic: K-Motives and Koszul Duality in Geometric Representation Theory Speaker: Jens Eberhardt Affiliation: Max Planck Institute Date: April 07, 2021 For m
From playlist Mathematics
Winter School JTP: Introduction to A-infinity structures, Bernhard Keller, Lecture 3
In this minicourse, we will present basic results on A-infinity algebras, their modules and their derived categories. We will start with two motivating problems from representation theory. Then we will briefly present the topological origin of A-infinity structures. We will then define and
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Lie Algebras and Homotopy Theory - Jacob Lurie
Members' Seminar Topic: Lie Algebras and Homotopy Theory Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: November 11, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
A geometric model for the bounded derived category of a gentle algebra, Sibylle Schroll Lecture 2
Gentle algebras are quadratic monomial algebras whose representation theory is well understood. In recent years they have played a central role in several different subjects such as in cluster algebras where they occur as Jacobian algebras of quivers with potentials obtained from triangula
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
A geometric model for the bounded derived category of a gentle algebra, Sibylle Schroll Lecture 3
Gentle algebras are quadratic monomial algebras whose representation theory is well understood. In recent years they have played a central role in several different subjects such as in cluster algebras where they occur as Jacobian algebras of quivers with potentials obtained from triangula
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Michael Mandell: The strong Kunneth theorem for topological periodic cyclic homology
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Hesselholt has recently been advertising "topological periodic cyclic homology" (TP) as potentially filling some of the same roles for finite primes as periodic cyclic homology plays
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Geordie Williamson. Some examples of Koszul duality via dg algebras
Seminar talk on CORONA GS: https://murmuno.mit.edu/coronags Abstract: I will explain the basics of Morita theory for derived categories and give some examples, including the classic BGG duality between symmetric and exterior algebras. This is standard stuff but should perhaps be better kn
From playlist CORONA GS
Osamu Iyama: Preprojective algebras and Cluster categories
Abstract: The preprojective algebra P of a quiver Q has a family of ideals Iw parametrized by elements w in the Coxeter group W. For the factor algebra Pw=P/Iw, I will discuss tilting and cluster tilting theory for Cohen-Macaulay Pw-modules following works by Buan-I-Reiten-Scott, Amiot-Rei
From playlist Combinatorics
Lecture 11: Negative Topological cyclic homology
Correction: In the definition of stable ∞-categories at the very beginning, we forgot the condition that C has a zero object, i.e. the initial and terminal objects agree via the canonical morphism between them. Sorry for the confusion! In this video we define negative topological cyclic h
From playlist Topological Cyclic Homology
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)
algebraic geometry 23 Categories
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a quick review of category theory as background for the definition of morphisms of algebraic varieties.
From playlist Algebraic geometry I: Varieties