Functors | Homological algebra
In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. (Wikipedia).
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
A (proper) introduction to derived CATegories
While there are introductions to derived categories that are more sensible for practical aspects, in this video I give the audience of taste of what's involved in the proper, formal definition of derived categories. Special thanks to Geoff Vooys, whose notes (below) inspired this video: ht
From playlist Miscellaneous Questions
We give a buttload of definitions for morphisms on various categories of complexes. The derived category of an abelian category is a category whose objects are cochain complexes and whose morphisms I describe in this video.
From playlist Derived Categories
Higher Algebra 7: Non-abelian derived functors
In this video, we discuss the notion of non-abelian derived functors and Animation. Along the way, we discuss the Yoneda lemma. Warning: The Yoneda exercises stated at 35:00 is a bit hard given the technology we have, so I recommend simply proving the analogous statement for ordinary cat
From playlist Higher Algebra
Summary for combining rational expressions
Learn how to add/subtract rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. When adding or subtracting rational expressions we first obtain the lowest common multiple (LCM) of th
From playlist Add and Subtract Rational Expressions
The dependent product as universal construction
In this video I elaborate on the general arrow theoretic characterization of dependent product (or the dependent product functor) that exists in a Cartesian closed category. This is the dependent product that gives dependent product types its name, and it arises in concrete cases in geomet
From playlist Logic
Factoring out the GCF to simplify the rational expression
Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational
From playlist Simplify Rational Expressions (Binomials) #Rational
Simplify a rational expression
Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational
From playlist Simplify Rational Expressions (Binomials) #Rational
Simplify a rational expression
Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational
From playlist Simplify Rational Expressions (Binomials) #Rational
Lecture 6: HKR and the cotangent complex
In this video, we discuss the cotangent complex and give a proof of the HKR theorem (in its affine version) 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-m
From playlist Topological Cyclic Homology
ITHT: Part 10- Derived Functors
Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#DerivedFunctors Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtub... Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name:
From playlist Introduction to Homotopy Theory
Felix Klein Lecture 2022 part6
From playlist Felix Klein Lectures 2022
Derived categories of cyclic covers and their branch divisors - Alexander Perry
Alexander Perry Harvard University April 29, 2015 Given a variety YY with a rectangular Lefschetz decomposition of its derived category, I will discuss an interesting relation between the derived categories of a cyclic cover of YY and its branch divisor. As examples, I will describe the c
From playlist Mathematics
Learn to solve an equation raised to a rational power
👉 Learn how to deal with Rational Powers or Exponents. Exponents are shorthand for repeated multiplication of the same thing by itself. This process of using exponents is called "raising to a power", where the exponent is the "power". Rational exponents are exponents that are fractions. To
From playlist Solve Equations with Fractional Exponents