Adjoint functors | Monoidal categories

Monoidal adjunction

Suppose that and are two monoidal categories. A monoidal adjunction between two lax monoidal functors and is an adjunction between the underlying functors, such that the natural transformations and are monoidal natural transformations. (Wikipedia).

Video thumbnail

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

Video thumbnail

Monotone Expanders - Constructions and Applications - Zeev Dvir

Monotone Expanders -- Constructions and Applications Zeev Dvir Princeton University; Member, School of Mathematics April 22, 2011 A Monotone Expander is an expander graph which can be decomposed into a union of a constant number of monotone matchings, under some fixed ordering of the verti

From playlist Mathematics

Video thumbnail

How to Multiply Two Monomials by a Trinomial and Binomial

👉 Learn how to multiply polynomials. We apply the distributive property to polynomials by multiplying a monomial to every term in a polynomial. When multiplying monomials it is important that we multiply the coefficients and apply the rules of exponents to add the powers of each variable.

From playlist How to Multiply Polynomials

Video thumbnail

Paul-André Melliès - A Functorial Excursion between Algebraic Geometry and Linear Logic

In this talk, I will use the functor of points approach to Algebraic Geometry to establish that every covariant presheaf X on the category of commutative rings — and in particular every scheme X — comes equipped “above it” with a symmetric monoidal closed category PshModX of presheaves of

From playlist Combinatorics and Arithmetic for Physics: special days

Video thumbnail

Ivo Dell’Ambrogio: A survey of Mackey and Green 2-functors

CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 23, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR

From playlist Topology

Video thumbnail

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

Video thumbnail

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

Video thumbnail

Lecture 11: Negative Topological cyclic homology

Correction: In the definition of stable ∞-categories at the very beginning, we forgot the condition that C has a zero object, i.e. the initial and terminal objects agree via the canonical morphism between them. Sorry for the confusion! In this video we define negative topological cyclic h

From playlist Topological Cyclic Homology

Video thumbnail

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

Video thumbnail

How to Multiply a Monomial by a Trinomial Polynomial Product

👉 Learn how to multiply polynomials. We apply the distributive property to polynomials by multiplying a monomial to every term in a polynomial. When multiplying monomials it is important that we multiply the coefficients and apply the rules of exponents to add the powers of each variable.

From playlist How to Multiply Polynomials

Video thumbnail

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

Video thumbnail

Monotonicity Theorem

Using the monotonicity theorem to determine when a function is increasing or decreasing.

From playlist Calculus

Video thumbnail

Stable Homotopy Seminar, 8: The Stable Model Category of Spectra

We discuss the enrichment of spectra over spaces, and the compatibility of this enrichment with the model structure. Then we define the stable model structure by adding extra cofibrations to the levelwise model category of spectra, and restricting the weak equivalences to those maps which

From playlist Stable Homotopy Seminar

Video thumbnail

Using the Box Method to Multiply a Monomial by a Trinomial

👉 Learn how to multiply polynomials. We apply the distributive property to polynomials by multiplying a monomial to every term in a polynomial. When multiplying monomials it is important that we multiply the coefficients and apply the rules of exponents to add the powers of each variable.

From playlist How to Multiply Polynomials

Video thumbnail

How to Multiply a Monomial by a Trinomial Using Distributive Property

👉 Learn how to multiply polynomials. We apply the distributive property to polynomials by multiplying a monomial to every term in a polynomial. When multiplying monomials it is important that we multiply the coefficients and apply the rules of exponents to add the powers of each variable.

From playlist How to Multiply Polynomials

Video thumbnail

Higher Algebra 8: Spectra

In this video, we introduce and discuss spectra (in the sense of homotopy theory). We explain how they generalise abelian groups. 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 informa

From playlist Higher Algebra

Video thumbnail

Stable Homotopy Theory by Samik Basu

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

Video thumbnail

Yonatan Harpaz - New perspectives in hermitian K-theory II

Warning: around 32:30 in the video, in the slide entitled "Karoubi's conjecture", a small mistake was made - in the third bulleted item the genuine quadratic structure appearing should be the genuine symmetric one (so both the green and red instances of the superscript gq should be gs), an

From playlist New perspectives on K- and L-theory

Video thumbnail

Multiply a Monomial by a Trinomial - Free Math Help Videos

👉 Learn how to multiply polynomials. We apply the distributive property to polynomials by multiplying a monomial to every term in a polynomial. When multiplying monomials it is important that we multiply the coefficients and apply the rules of exponents to add the powers of each variable.

From playlist How to Multiply Polynomials

Related pages

Adjoint functors | Monoidal monad | Monoidal category | Monoidal natural transformation | Natural transformation