In category theory, a branch of mathematics, the formal criteria for adjoint functors are criteria for the existence of a left or right adjoint of a given functor. One criterion is the following, which first appeared in Peter J. Freyd's 1964 book Abelian Categories, an Introduction to the Theory of Functors: Freyd's adjoint functor theorem โ Let be a functor between categories such that is complete. Then the following are equivalent (for simplicity ignoring the set-theoretic issues): 1. * G has a left adjoint. 2. * preserves all limits and for each object x in , there exist a set I and an I-indexed family of morphisms such that each morphism is of the form for some morphism . Another criterion is: Kan criterion for the existence of a left adjoint โ Let be a functor between categories. Then the following are equivalent. 1. * G has a left adjoint. 2. * G preserves limits and, for each object x in , the limit exists in . 3. * The right Kan extension of the identity functor along G exists and is preserved by G. Moreover, when this is the case then a left adjoint of G can be computed using the left Kan extension. (Wikipedia).
Simplifying the sum of two rational expressions with like denominators
๐ Learn how to add and subtract rational expressions by applying the rules of exponents. When adding and subtracting rational expressions we need to have common denominators. To obtain common denominators we will need to multiply the numerator and the denominator of the rational expression
From playlist Simplify Using the Rules of Exponents
Introduction to the Distributive Property
This video explains the distributive property and provides examples on how to use the distributive property. http://mathispower4u.yolasite.com/
From playlist The Distributive Property and Simplifying Algebraic Expressions
Using the property of exponents to multiply expressions
๐ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac
From playlist Simplify Using the Rules of Exponents
Ex: Quotient and Negative Exponent Properties
This video explains how to simplify a quotient using the quotient property of exponents and the negative exponent property of exponents.
From playlist Properties of Exponents
Simplifying expressions using the rules of exponents, quotient property
๐ Learn how to simplify expressions using the quotient rule and the negative exponent rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the expon
From playlist Simplify Using the Rules of Exponents
Higher Algebra 6: Derived Functors
In this video, we define and discuss derived functors between derived categories of abelian categories. Additionally we discuss the notion of adjoint functors and Kan extensions. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.
From playlist Higher Algebra
Simplifying a rational expression
๐ Learn how to simplify expressions using the quotient rule and the negative exponent rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the expon
From playlist Simplify Using the Rules of Exponents
Simplify an expression by applying the power to quotient rule of exponents
๐ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac
From playlist Simplify Using the Rules of Exponents
รtale cohomology 9/10/2020 Part 1
Enough injectives, derived functors
From playlist รtale cohomology and the Weil conjectures
Friedrich Wagemann: Deformation quantization of Leibniz algebras
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
How to use properties of exponents to simplify an expression
๐ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac
From playlist Simplify Using the Rules of Exponents
Laurent Lafforgue - 1/4 Classifying toposes of geometric theories
Course at the school and conference โToposes onlineโ (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Marc Levine: The rational motivic sphere spectrum and motivic Serre finiteness
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
David Nadler: Betti Langlands in genus one
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Introduction to Witt vectors, delta-rings, and prisms (Lecture 2) by James Borger
PERFECTOID SPACES ORGANIZERS : Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri and Narasimha Kumar Cheraku DATE & TIME : 09 September 2019 to 20 September 2019 VENUE : Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknat
From playlist Perfectoid Spaces 2019
In this video I talk about a beautiful family of adjoint functors between module categories, and how these offer a natural inspiration for the definitions of induced representation, and Frobenius reciprocity.
From playlist Miscellaneous Questions
Learn how to simplify an expression by applying the quotient rule of exponents
๐ Learn how to simplify expressions using the quotient rule and the negative exponent rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the expon
From playlist Simplify Using the Rules of Exponents
Perverse schobers and semi-orthogonal decompositions - Mikhail Kapranov
Vladimir Voevodsky Memorial Conference Topic: Perverse schobers and semi-orthogonal decompositions Speaker: Mikhail Kapranov Affiliation: Institute for Advanced Study Date: September 14, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Adding two rational expressions with the same denominators
๐ Learn how to add and subtract rational expressions by applying the rules of exponents. When adding and subtracting rational expressions we need to have common denominators. To obtain common denominators we will need to multiply the numerator and the denominator of the rational expression
From playlist Simplify Using the Rules of Exponents
Moduli of Representations and Pseudorepresentations - Carl Wang Erickson
Carl Wang Erickson Harvard University May 2, 2013 A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli
From playlist Mathematics