This is a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.) * Notes on foundations: In many expositions (e.g., Vistoli), the set-theoretic issues are ignored; this means, for instance, that one does not distinguish between small and large categories and that one can arbitrarily form a localization of a category. Like those expositions, this glossary also generally ignores the set-theoretic issues, except when they are relevant (e.g., the discussion on accessibility.) Especially for higher categories, the concepts from algebraic topology are also used in the category theory. For that see also glossary of algebraic topology. The notations and the conventions used throughout the article are: * [n] = {0, 1, 2, …, n}, which is viewed as a category (by writing .) * Cat, the category of (small) categories, where the objects are categories (which are small with respect to some universe) and the morphisms functors. * Fct(C, D), the functor category: the category of functors from a category C to a category D. * Set, the category of (small) sets. * sSet, the category of simplicial sets. * "weak" instead of "strict" is given the default status; e.g., "n-category" means "weak n-category", not the strict one, by default. * By an ∞-category, we mean a quasi-category, the most popular model, unless other models are being discussed. * The number zero 0 is a natural number. (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: 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
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
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
OWASP AppSec USA 2010: OWASP Secure Coding Practices Quick Reference Guide 1/2
Speaker: Keith Turpin, Boeing More information can be found on the OWASP website: http://bit.ly/hY4bqh Source: http://bit.ly/owasp_appsec_us_2010
From playlist OWASP AppSec USA 2010
Wolfram Physics Project: One Month Update
This is a Wolfram Physics Project one-month update. Begins at 2:37 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/physics-announcement Find the
From playlist Wolfram Physics Project Livestream Archive
Bad Math Glossary, or Soviet Propaganda?
A review of "The Algebra Tutor, Algebra 1 and Algebra 2, Volume 1". A textbook/workbook by Willie L. Thomas. It has a great propaganda-esque cover design, and a very finicky glossary to put it nicely. #mathbook #math 00:00 Rest of the Review 19:33 The Bad Glossary 23:00 End Buy a copy o
From playlist The Math Library
With Knowledge Doubt Increases - The Significance of Knowledge in Knowledge Graphs
Keynote at 6th International Conference on Graphs and Networks in the Humanities 2022 Prof. Dr. Harald Sack FIZ Karlsruhe - Leibniz Institute for Informaation Infrastructure Karlsruhe Institute of Technology Slides: https://bit.ly/WithKnowledgeDoubtIncreases FIZ ISE on twitter: https:/
From playlist ISE Conference Talks
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
Dark Matter - II (Lecture 1) by Neal Weiner
PROGRAM LESS TRAVELLED PATH OF DARK MATTER: AXIONS AND PRIMORDIAL BLACK HOLES (ONLINE) ORGANIZERS: Subinoy Das (IIA, Bangalore), Koushik Dutta (IISER, Kolkata / SINP, Kolkata), Raghavan Rangarajan (Ahmedabad University) and Vikram Rentala (IIT Bombay) DATE: 09 November 2020 to 13 Novemb
From playlist Less Travelled Path of Dark Matter: Axions and Primordial Black Holes (Online)
O'Reilly Webcast: Cyborg Anthropology: A Short Introduction
Cyborg Anthropology is a way of understanding how we live as technosocially connected citizens in the modern era. Our cell phones, cars and laptops have turned us into cyborgs. What does it mean to extend the body into hyperspace? What are the implications to privacy, information and the f
From playlist O'Reilly Webcasts
O'Reilly Webcast: Stylish Structure- XML Publishing with Adobe InDesign
*Note: Audio quality not very clear Traditional XML publishing uses XSLT to make web pages and XSL-FO to make printable PDFs from XML sources. Book and magazine publishers are frustrated by the limited styling and "untweakable" output of the PDF process. Adobe InDesign offers a more flexi
From playlist O'Reilly Webcasts 2
Histories and Models of Dark Matter - Neal Weiner
Solutions of the Strong CP Problem: An Assessment - Michael Dine Prospects in Theoretical Physics Particle Physics at the LHC and Beyond Topic: Histories and Models of Dark Matter Speaker: Neal Weiner Date: July 18th, 2017
From playlist PiTP 2017
Representations of finite groups of Lie type (Lecture 1) by Dipendra Prasad
PROGRAM : GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fun
From playlist Group Algebras, Representations And Computation
Category theory for JavaScript programmers #19: some formality around categories
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
How to turn a few Numbers into Worlds (Fractal Perlin Noise)
Creating even a modest world for a video game is a huge undertaking. However, games like Minecraft, Factorio, Terraria, Valheim and many more serve up fresh worlds with the click of a button. How do they do this? In this video, you’ll learn the inner workings of one of the foundational pil
From playlist Summer of Math Exposition 2 videos