In algebra, Quillen's Q-construction associates to an exact category (e.g., an abelian category) an algebraic K-theory. More precisely, given an exact category C, the construction creates a topological space so that is the Grothendieck group of C and, when C is the category of finitely generated projective modules over a ring R, for , is the i-th K-group of R in the classical sense. (The notation "+" is meant to suggest the construction adds more to the classifying space BC.) One puts and call it the i-th K-group of C. Similarly, the i-th K-group of C with coefficients in a group G is defined as the homotopy group with coefficients: . The construction is widely applicable and is used to define an algebraic K-theory in a non-classical context. For example, one can define equivariant algebraic K-theory as of of the category of equivariant sheaves on a scheme. Waldhausen's S-construction generalizes the Q-construction in a stable sense; in fact, the former, which uses a more general Waldhausen category, produces a spectrum instead of a space. also gives a construction of algebraic K-theory for exact categories. See also module spectrum#K-theory for a K-theory of a ring spectrum. (Wikipedia).
Building A Product From The Ground Up
For most seasoned business owners and aspiring entrepreneurs, the product development process often carries a mystical aura. Product development refers to the complete process of taking a product to market. It also covers renewing an existing product and introducing an old product to a new
From playlist Product Development
What's the difference between concrete and cement? Concrete is the most important construction material on earth and foundation of our modern society. At first glance it seems rudimentary, but there is a tremendous amount of complexity involved in every part of designing and placing conc
From playlist Civil Engineering
How engineers build different bridges
Do you know how engineers build different types of bridges for different situations? From arch bridges and beam bridges to suspension bridges and movable bridges, here is all you need to know about the technology behind them. To get the latest science and technology news, subscribe to o
From playlist Theory to Reality
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
Mankind has been building skyscrapers and similar tall buildings for decades now. 👷👨‍🏠Ever wonder how those sky-piercing buildings withstand high-winds without falling over or how they are built so fast? ⏱ In this video, you will learn how skyscrapers are built and how skyscrapers came
From playlist Engineering Wonders
Written in 1939. Utilizes all metal instruments. A masterpiece.
From playlist experimental classical
Geometry - Constructions (1 of 15) How to Draw Line Segments of the Same Length
Visit http://ilectureonline.com for more math and science lectures! In this video I will demonstrate how to draw line segments of the same length. Next video in the Constructions series can be seen at: http://youtu.be/hglhedZs41Y
From playlist GEOMETRY 2 - CONSTRUCTIONS
Why Buildings Need Foundations
What the heck is a foundation and why do all structures need one? The bundle deal with Curiosity Stream has ended, but you can still get a great discount on Nebula and support Practical Engineering here: https://go.nebula.tv/practical-engineering If all the earth was solid rock, life woul
From playlist Civil Engineering
Truss Bridge Project - simple, fundamental engineering project for kids
Be sure to check out www.stem-inventions.com Hanging scale: https://amzn.to/2Q3cYNO
From playlist Bridge Building
Maria Montanucci: Algebraic curves with many rational points over finite fields
CONFERENCE Recording during the thematic meeting : « Conference On alGebraic varieties over fiNite fields and Algebraic geometry Codes» the February 13, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks
From playlist Algebraic and Complex Geometry
Linear Algebra 23b: How to Determine the Matrices Q and S in the Polar Decomposition
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Visual Group Theory, Lecture 6.8: Impossibility proofs
Visual Group Theory, Lecture 6.8: Impossibility proofs The ancient Greeks sought basic ruler and compass constructions such as (1) squaring the circle, (2) doubling the cube, and (3) trisecting an angle. In the previous lecture, we learned how a length or angle 'z' is constructable iff th
From playlist Visual Group Theory
Nero Budur: ​Absolute sets and the Decomposition Theorem
Abstract: We give a new, more conceptual proof of the Decomposition Theorem for semisimple perverse sheaves of rank-one origin, assuming it for those of constant-sheaf origin, that is, assuming the geometric case proven by Beilinson-Bernstein-Deligne-Gabber. Joint work with Botong Wang. R
From playlist Algebraic and Complex Geometry
4. Forbidding a subgraph III: algebraic constructions
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX How does one construct graphs that do not contain complet
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
p-adic Asai transfer by Baskar Balasubramanyam
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Eisenstein Congruences and Euler Systems - Eric Urban
Eisenstein Congruences and Euler Systems Eric Urban Columbia University; Member, School of Mathematics February 10, 2011 GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
From playlist Mathematics
Jean-Luc Thiffeault: "On mix-norms and the rate of decay of correlations"
Transport and Mixing in Complex and Turbulent Flows 2021 "On mix-norms and the rate of decay of correlations" Jean-Luc Thiffeault - University of Wisconsin-Madison, Mathematics Abstract: Two quantitative notions of mixing are the decay of correlations and the decay of a mix-norm --- a ne
From playlist Transport and Mixing in Complex and Turbulent Flows 2021
Motivic correlators and locally symmetric spaces - Alexander Goncharov
Locally Symmetric Spaces Seminar Topic: Motivic correlators and locally symmetric spaces Speaker: Alexander Goncharov Affiliation: Yale University; Member, School of Mathematics and Natural Sciences Date: October 3, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Representations of finite groups of Lie type (Lecture 1) by Dipendra Prasad
PROGRAM : GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fun
From playlist Group Algebras, Representations And Computation
Geometry - Constructions (2 of 15) How to Draw Angles of the Same Measure
Visit http://ilectureonline.com for more math and science lectures! In this video I will demonstrate how to draw exact angles of the same measure. Next video in the Constructions series can be seen at: http://youtu.be/2yBv2rIUeNg
From playlist GEOMETRY 2 - CONSTRUCTIONS