Algebraic structures | Category theory | Semigroup theory
In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of mathematics. The functions from a set into itself form a monoid with respect to function composition. More generally, in category theory, the morphisms of an object to itself form a monoid, and, conversely, a monoid may be viewed as a category with a single object. In computer science and computer programming, the set of strings built from a given set of characters is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for process calculi and concurrent computing. In theoretical computer science, the study of monoids is fundamental for automata theory (Krohn–Rhodes theory), and formal language theory (star height problem). See semigroup for the history of the subject, and some other general properties of monoids. (Wikipedia).
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
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
Monoids are everywhere in mathematics, but what are they? And why are they so useful? This video uses a simple example to show you exactly what the 4 rules of monoids are all about. I made this video for the 2021 Summer of Math Exposition. Enjoy! If you like this content, you can supp
From playlist Summer of Math Exposition Youtube Videos
Category Theory 10.2: Monoid in the category of endofunctors
Monad as a monoid in the category of endofunctors
From playlist Category Theory
Math 031 031017 Monotone Sequence Theorem
The rational numbers have holes: square root of 2 is irrational. Bounded sequences; bounded above, bounded below. Q. Does bounded imply convergent? (No.) Q. Does convergent imply bounded? (Yes.) Proof that convergent implies bounded. Statement of Monotone Sequence Theorem. Definition
From playlist Course 3: Calculus II (Spring 2017)
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
Nadia Larsen: Equilibrium states for C*-algebras of right LCM monoids.
Talk by Nadia Larsen in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on October 13, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Andy Magid, University of Oklahoma
Andy Magid, University of Oklahoma Differential Brauer Monoids
From playlist Online Workshop in Memory of Ray Hoobler - April 30, 2020
Matt SZCZESNY - Toric Hall Algebras and infinite-dimentional Lie algebras
The process of counting extensions in categories yields an associative (and sometimes Hopf) algebra called a Hall algebra. Applied to the category of Feynman graphs, this process recovers the Connes-Kreimer Hopf algebra. Other examples abound, yielding various combinatorial Hopf algebras.
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Category theory for JavaScript programmers #24: monoidal functors
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Is it a monomial, binomial, trinomial, or polynomial
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Morgan Rogers - Toposes of Topological Monoid Actions
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RogersSlidesToposesOnline.pdf We explain the properties of the familiar properties of continuous actions of groups o
From playlist Toposes online