Homological algebra | Categories in category theory
In mathematics, especially homological algebra, a differential graded category, often shortened to dg-category or DG category, is a category whose morphism sets are endowed with the additional structure of a differential graded -module. In detail, this means that , the morphisms from any object A to another object B of the category is a direct sum and there is a differential d on this graded group, i.e., for each n there is a linear map , which has to satisfy . This is equivalent to saying that is a cochain complex. Furthermore, the composition of morphisms is required to be a map of complexes, and for all objects A of the category, one requires . (Wikipedia).
(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
What are differential equations?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Differential equations are usually classified into two general categories: partial differential equations, which are also called partial derivatives, and ordinary differential equations. Part
From playlist Popular Questions
(0.3) Lesson: 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
Introduction to differential equations | Lecture 1 | Differential Equations for Engineers
Classification of differential equations into ode/pde, order, linear/nonlinear. Some examples are explained. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Subs
From playlist Differential Equations for Engineers
Introduction to Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to Differential Equations - The types of differential equations, ordinary versus partial. - How to find the order of a differential equation.
From playlist Differential Equations
Introduction to Differential Equation Terminology
This video defines a differential equation and then classifies differential equations by type, order, and linearity. Search Library at http://mathispower4u.wordpress.com
From playlist Introduction to Differential Equations
Differential Equatons: Find the Order and Classify as Linear or Nonlinear
This video explains how to determine the order of a differential equation and how to determine if it is linear or nonlinear. http://mathispower4u.com
From playlist Introduction to Differential Equations
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
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"
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"
A01 Introduction to linear systems
An introduction to linear sets of ordinary differential equations.
From playlist A Second Course in Differential Equations
On the notion of λ-connection - Carlos Simpson
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Carlos Simpson University of Nice October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a four-day confe
From playlist Pierre Deligne 61st Birthday
Winter School JTP: Introduction to A-infinity structures, Bernhard Keller, Lecture 1
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"
Non-commutative motives - Maxim Kontsevich
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Maxim Kontsevich Institute for Advanced Study October 20, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a fo
From playlist Pierre Deligne 61st Birthday
Linear versus Nonlinear Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Linear versus Nonlinear Differential Equations
From playlist Differential Equations
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
2-Verma modules - Gregoire Naisse; Pedro Vaz
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: 2-Verma modules Speakers: Gregoire Naisse; Pedro Vaz Affiliation: University College London; University College London Date: November 18, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
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
Types Of Differential Equations
Introduction to the Order of a differential equation and the idea of Linear and Non-linear differential equations. Discussion of how the number of constants of a general solution is related to the order of a differential equation.
From playlist Mathematical Physics I Uploads
Ben Elias: Categorifying Hecke algebras at prime roots of unity
Thirty years ago, Soergel changed the paradigm with his algebraic construction of the Hecke category. This is a categorification of the Hecke algebra at a generic parameter, where the parameter is categorified by a grading shift. One key open problem in categorification is to categorify He
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification