Coalgebras | Monoidal categories | Bialgebras
In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a counital coassociative coalgebra. The algebraic and coalgebraic structures are made compatible with a few more axioms. Specifically, the comultiplication and the counit are both unital algebra homomorphisms, or equivalently, the multiplication and the unit of the algebra both are coalgebra morphisms. (These statements are equivalent since they are expressed by the same commutative diagrams.) Similar bialgebras are related by bialgebra homomorphisms. A bialgebra homomorphism is a linear map that is both an algebra and a coalgebra homomorphism. As reflected in the symmetry of the commutative diagrams, the definition of bialgebra is self-dual, so if one can define a dual of B (which is always possible if B is finite-dimensional), then it is automatically a bialgebra. (Wikipedia).
In this video on topics in emergency surgery for medical students and doctors, I discuss the common condition of biliary colic. Watch this video if your are preparing for the exams or are seeing a patient with biliary colic. Biliary colic is the most common form of gallstone disease, an
From playlist Let's talk Surgery
Loïc FOISSY - Cointeracting Bialgebras
Pairs of cointeracting bialgebras recently appears in the literature of combinatorial Hopf algebras, with examples based on formal series, on trees (Calaque, Ebrahimi-Fard, Manchon), graphs (Manchon), posets... We will give several results obtained on pairs of cointeracting bialgebras: act
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Pavel Etingof: Poisson-Lie groups and Lie bialgebras - Lecture 1
HYBRID EVENT Recorded during the meeting "Lie Theory and Poisson Geometry" the January 10, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiov
From playlist Virtual Conference
Yvain BRUNED - Bogoliubov Type Recursions for Renormalisation in Regularity Structures
Hairer's regularity structures transformed the solution theory of singular stochastic partial differential equations. The notions of positive and negative renormalisation are central and the intricate interplay between these two renormalisation procedures is captured through the combinatio
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Topological interpretations of knots, curves & more
International visitors from Toronto visited SMRI to work on a topological algebra project with University of Sydney mathematician Dr Zsuzsanna Dancso. Professor Dror Bar-Natan (University of Toronto), Dr Nancy Scherich (Elon University) and PhD candidate Jessica Liu (University of Toronto)
From playlist SMRI Interviews
What is BIM? (Building Information Modelling) - NBS National BIM Library
This video helps with the question: 'What is BIM'? http://www.nationalBIMlibrary.com is the construction industry's free-to-use resource of NBS standard BIM content. Objects are available in IFC, ArchiCAD, Bentley, Revit and Vectoworks format. NBS National BIM Library content links with
From playlist The World's Best BIM Videos | Curated by The B1M
A very quick demo of how to access the 2D and 3D calculator on Geogebra.
From playlist Geogebra
Introducing the Concept of Congruence
From playlist GeoGebra Geometry
How to Create a GeoGebra Class from an Activity
More info: https://www.geogebra.org/m/hncrgruu#material/mxc255j6 #GeoGebra
From playlist GeoGebra Classroom: Quick Tutorials
Gérard H E Duchamp - Kleene Stars in Shuffle Algebras
We present some bialgebras and their monoid of characters. We entend, to the case of some rings, the well-known theorem (in the case when the scalars form a field) about linear independence of characters. Examples of algebraic independence of subfamilies and identites derived from their gr
From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020
quick review of how to resize an image in Geogebra
From playlist Geogebra
Pavel Etingof: Poisson-Lie groups and Lie bialgebras - Lecture 2
HYBRID EVENT Recorded during the meeting "Lie Theory and Poisson Geometry" the January 11, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiov
From playlist Virtual Conference
This playlist is for patients and those interested in learning more about emergency surgical conditions and procedures. I am Dr Juan Klopper, a consultant surgeon at Groote Schuur Hospital and Head of Surgical Education at the University of Cape Town in South Africa. This video contains
From playlist Surgical information for patients
Pavel Etingof: Poisson-Lie groups and Lie bialgebras - Lecture 3
HYBRID EVENT Recorded during the meeting "Lie Theory and Poisson Geometry" the January 12, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiov
From playlist Virtual Conference