Symmetric monoidal category

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

Higher Algebra 9: Symmetric monoidal infinity categories

In this video, we introduce the notion of a symmetric monoidal infinity categories and give some examples. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-mu

From playlist Higher Algebra

Category Theory 7.2: Monoidal Categories, Functoriality of ADTs, Profunctors

From playlist Category Theory

Symmetric Groups (Abstract Algebra)

Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in

From playlist Abstract Algebra

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

Stable Homotopy Seminar, 13: The Smash Product

I describe a bunch of desirable properties of the smash product on spectra, and then prove Lewis's theorem that no category of spectra has them. However, there are ways of sacrificing one or the other of the properties and getting something fairly well-behaved. The earliest attempts are Bo

From playlist Stable Homotopy Seminar

Symmetric groups

In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto

From playlist Abstract algebra

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

Higher Algebra 10: E_n-Algebras

In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin

From playlist Higher Algebra

Lecture 7: Hochschild homology in ∞-categories

In this video, we construct Hochschild homology in an arbitrary symmetric-monoidal ∞-category. The most important special case is the ∞-category of spectra, in which we get Topological Hochschild homology. Feel free to post comments and questions at our public forum at https://www.uni-mu

From playlist Topological Cyclic Homology

Eugenia Cheng: "The periodic table of n-categories"

Speaker: Eugenia Cheng (University of Sheffield) Title: The periodic table of n-categories Event: Categories, Logic and Foundations of Physics IV (January 2009, Imperial College London) Slides: http://www.cs.ox.ac.uk/quantum/slides/clap4-eugeniacheng.pdf Abstract: Degenerate n-categories

From playlist Software Development Lectures

On the classification of fusion categories – Sonia Natale – ICM2018

Algebra Invited Lecture 2.5 On the classification of fusion categories Sonia Natale Abstract: We report, from an algebraic point of view, on some methods and results on the classification problem of fusion categories over an algebraically closed field of characteristic zero. © Interna

From playlist Algebra

Alon Nissan-Cohen: Towards an ∞-categorical version of real THH

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Following Hesselholt and Madsen's development of the so-called "real" (i.e. Z/2-equivariant) version of algebraic K-theory, Dotto developed a th

From playlist HIM Lectures: Junior Trimester Program "Topology"

Category theory for JavaScript programmers #27: string diagrams

http://jscategory.wordpress.com/source-code/

From playlist Category theory for JavaScript programmers

Representation Theory & Categorification II - Catharina Stroppel

2021 Women and Mathematics - Uhlenbeck Course Lecture Topic: Representation Theory & Categorification II Speaker: Catharina Stroppel Affiliation: University of Bonn Date: May 25, 2021 In modern representation theory we often study the category of modules over an algebra, in particular i

From playlist Mathematics

Higher Algebra 13: The Tate diagonal

In this video we discuss the Tate diagonal, which is a surprising feature of the world of spectra. For further details on this construction, see https://arxiv.org/pdf/1707.01799.pdf, section III.1. Feel free to post comments and questions at our public forum at https://www.uni-muenster

From playlist Higher Algebra

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