In category theory, a monoidal monad is a monad on a monoidal category such that the functor is a lax monoidal functor and the natural transformations and are monoidal natural transformations. In other words, is equipped with coherence maps and satisfying certain properties (again: they are lax monoidal), and the unit and multiplication are monoidal natural transformations. By monoidality of , the morphisms and are necessarily equal. All of the above can be compressed into the statement that a monoidal monad is a monad in the 2-category of monoidal categories, lax monoidal functors, and monoidal natural transformations. (Wikipedia).
Category Theory 10.2: Monoid in the category of endofunctors
Monad as a monoid in the category of endofunctors
From playlist Category Theory
Geometry of Frobenioids - part 2 - (Set) Monoids
This is an introduction to the basic properties of Monoids. This video intended to be a starting place for log-schemes, Mochizuki's IUT or other absolute geometric constructions using monoids.
From playlist Geometry of Frobenioids
Okay but WTF is a MONAD?????? #SoME2
"A monad is a monoid in the category of endofunctors" Words dreamed up by the utterly insane!!! In this video I go over the common meme and explain it's origins and show many examples of monads out in the wild! This video is intended for anyone with programming experience who wants to fin
From playlist Summer of Math Exposition 2 videos
What is the definition of a monomial and polynomials with examples
👉 Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas classifying polynomials by the degree will focus on
From playlist Classify Polynomials
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
Determine if an Expression is a Polynomial
This video explains how to determine if an expression is a polynomial.
From playlist Introduction to Polynomials
RailsConf 2022 - Functional Programming in Plain Terms by Eric Weinstein
Have you ever wanted to know what a monad is? How about a functor? What about algebraic data types and parametric polymorphism? If you've been interested in these ideas but scared off by the language, you're not alone: for an approach that champions composing simple pieces, functional prog
From playlist RailsConf 2022
Polynomials - Classifying Monomials, Binomials & Trinomials - Degree & Leading Coefficient
This algebra video tutorial provides a basic introduction into polynomials. It explains how to identify a monomial, binomial, and a trinomial according to the number of terms present in an algebraic expression. it also explains how to identify all of the terms in a polynomial as well as
From playlist New Algebra Playlist
Category theory for JavaScript programmers #24: monoidal functors
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Shadows of Computation - Lecture 7 - Because it's there
Welcome to Shadows of Computation, an online course taught by Will Troiani and Billy Snikkers, covering the foundations of category theory and how it is used by computer scientists to abstract computing systems to reveal their intrinsic mathematical properties. In the seventh lecture Will
From playlist Shadows of Computation
Substructural Type Theory - Zeilberger
Noam Zeilberger IMDEA Software Institute; Member, School of Mathematics March 22, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Foundations S2 - Seminar 9 - Morgan Rogers on Morita equivalences and topological monoids
In this guest lecture, Morgan Rogers presents some results on topological monoids, topoi and Morita equivalences. Abstract: This talk presents the story which convinced me that logic has something positive to contribute in resolving questions in other areas of mathematics. Groups (and mor
From playlist Foundations seminar
ZuriHac 2016: Monad Homomorphisms
A Google TechTalk, July 23, 2016, presented by Edward Kmett ABSTRACT: The way that we use the monad transformer library today leads to code that has pathological performance problems. Can we do better? https://wiki.haskell.org/ZuriHac2016
From playlist ZuriHac 2016
Brian Beckman: Don't fear the Monad
Cross posted from msdn's channel 9. Functional programming is increasing in popularity these days given the inherent problems with shared mutable state that is rife in the imperative world. As we march on to a world of multi and many-core chipsets, software engineering must evolve to bett
From playlist Software Development Lectures
Monads are a uniquely powerful tool for solving common problems in your programs. If we can cut through all the jargon and notation, we really supercharge our problem-solving with monads. Kyle will help us solve our monad problems! EVENT / SPEAKER: ThunderPlains 2020 / Kyle Simpson PUBLI
From playlist Functional Programming
Functional programming design patterns by Scott Wlaschin
In object-oriented development, we are all familiar with design patterns such as the Strategy pattern and Decorator pattern, and design principles such as SOLID. The functional programming community has design patterns and principles as well. This talk will provide an overview of some of t
From playlist Software Development Lectures
Monodromy of nFn−1 hypergeometric functions and arithmetic groups II - Venkataramana
Speaker: T. N. Venkataramana (TIFR) Title: Monodromy of nFn−1 hypergeometric functions and arithmetic groups II We describe results of Levelt and Beukers-Heckman on the explicit computation of monodromy for generalised hypergeometric functions of one variable. We then discuss the question
From playlist Mathematics