In category theory, a branch of mathematics, a PROP is a symmetric strict monoidal category whose objects are the natural numbers n identified with the finite sets and whose tensor product is given on objects by the addition on numbers. Because of “symmetric”, for each n, the symmetric group on n letters is given as a subgroup of the automorphism group of n. The name PROP is an abbreviation of "PROduct and Permutation category". The notion was introduced by Adams and MacLane; the topological version of it was later given by Boardman and Vogt. Following them, J. P. May then introduced the notion of “operad”, a particular kind of PROP. There are the following inclusions of full subcategories: where the first category is the category of (symmetric) operads. (Wikipedia).
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 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
Category Theory 1.1 : Introduction to Categories/Metacategories
In this video, I introduce the ideas behind categories and metacategories; specifically their axioms and how they relate to the many structures we've covered before. Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=nMT44uK5ke0 Notes : None yet Patreon : https://ww
From playlist Category Theory
Marcy Robertson: Expansions, completions and automorphisms of welded tangled foams
SMRI Seminar: Marcy Robertson (University of Melbourne) Abstract: Welded tangles are knotted surfaces in R^4. Bar-Natan and Dancso described a class of welded tangles which have "foamed vertices" where one allows surfaces to merge and split. The resulting welded tangled foams carry an alg
From playlist SMRI Seminars
Feynman categories, universal operations and master equations - Ralph Kaufmann
Ralph Kaufmann Purdue University; Member, School of Mathematics December 6, 2013 Feynman categories are a new universal categorical framework for generalizing operads, modular operads and twisted modular operads. The latter two appear prominently in Gromov-Witten theory and in string field
From playlist Mathematics
Harm Derksen: "Invariant Tensors and Wheeled PROPs"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Invariant Tensors and Wheeled PROPs" Harm Derksen - Northeastern University, Mathematics Abstract: If we take a tensor
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Sheel Ganatra: The Floer theory of a cotangent bundle, the string topology of the base and...
Find other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies,
From playlist Jean-Morlet Chair - Lalonde/Teleman
Alex Fok, Equvariant twisted KK-theory of noncompact Lie groups
Global Noncommutative Geometry Seminar(Asia-Pacific), Oct. 25, 2021
From playlist Global Noncommutative Geometry Seminar (Asia and Pacific)
Working Group on Univalent Foundations - Michael Shulman
Michael Shulman Institute for Advanced Study December 12, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Ian talks about leveraging algebraic theory in JavaScript to create functional, structured code that is simple to test and demonstrates algebraic traits. EVENT: Vancouver Full Stack, 2019-09-17 SPEAKER: Ian Hofmann-Hicks PUBLICATION PERMISSIONS: Original video was published with the
From playlist JavaScript
On the Category of hSets - Bas Spitters
On the Category of hSets - Bas Spitters Bas Spitters Radboud University Nijmegen; Member, School of Mathematics April 3, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
Lecturer: Dr. Erin M. Buchanan Harrisburg University of Science and Technology Summer 2019 I think I got a little excited and talked a bit too close to the mic - sound gets a little loud here and there. Apologies! This video covers simple and multiple correspondence analysis. First, I st
From playlist Natural Language Processing
The Curtis-Hedlund-Lyndon Theorem | Nathan Dalaklis | math academic talks
This is the second seminar talk that I have given as a math phd student. It is an expository academic talk that I gave as a Math PhD student during my second semester of my second year in my PhD program. The talk concerns the Factors of Symbolic Dynamical Systems and is focused on the Curt
From playlist Academic 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