Category theory | Outlines of mathematics and logic
The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy certain basic conditions. Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories. (Wikipedia).
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
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
Intuitive Introduction to Category Theory
Category Theory offers a different style of thinking about mathematics. I describe how using functions and sets as examples. Join our Discord to engage with other Mathematics enthusiasts ! https://discord.gg/yyDzhKXUBV Patreon: https://www.patreon.com/MetaMaths Source code for animatio
From playlist Category Theory course
Category Theory: The Beginner’s Introduction (Lesson 1 Video 3)
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
PNWS 2014 - What every (Scala) programmer should know about category theory
By, Gabriel Claramunt Aren't you tired of just nodding along when your friends starts talking about morphisms? Do you feel left out when your coworkers discuss a coproduct endofunctor? From the dark corners of mathematics to a programming language near you, category theory offers a compac
From playlist PNWS 2014
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
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 9
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 15
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Alon Nissan-Cohen: Towards an ∞-categorical version of real THH
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Following Hesselholt and Madsen's development of the so-called "real" (i.e. Z/2-equivariant) version of algebraic K-theory, Dotto developed a th
From playlist HIM Lectures: Junior Trimester Program "Topology"
Christopher TOWNSEND - There are categories of ‘spaces' that are not categories of locales
Abstract We described a short list of categorical axioms that make a category behave like the category of locales. In summary the axioms assert that the category has an object that behaves like the Sierpnski space and this object is double exponentiable. A number of the usual results of lo
From playlist Topos à l'IHES
Spatial refinements and Khovanov homology – Robert Lipshitz & Sucharit Sarkar – ICM2018
Topology Invited Lecture 6.11 Spatial refinements and Khovanov homology Robert Lipshitz & Sucharit Sarkar Abstract: We review the construction and context of a stable homotopy refinement of Khovanov homology. © International Congress of Mathematicians – ICM www.icm2018.org Os direi
From playlist Topology
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 14
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Paul Arne Østvær: A1 contractible varieties
The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory"
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Alexei Davydov: Condensation of anyons in topological states of matter & structure theory
Condensation of anyons in topological states of matter and structure theory of E_2-algebras Abstract: The talk will be on the algebraic structure present in both parts of the title. This algebraic story is most pronounced for E2-algebras in the category of 2-vector spaces (also known as b
From playlist SMRI Seminars
From the Fukaya category to curve counts via Hodge theory - Nicholas Sheridan
Nicholas Sheridan Veblen Research Instructor, School of Mathematics September 26, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Category Theory: The Beginner’s Introduction (Lesson 1 Video 5)
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
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 22
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence