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4 results

  • 1 - An Introduction to Affine Lie Algebras and the Associated Groups

  • Shrawan Kumar, University of North Carolina, Chapel Hill
  • Book:
    Conformal Blocks, Generalized Theta Functions and the Verlinde Formula
    Published online:
    19 November 2021
    Print publication:
    25 November 2021, pp 1-67

  • Summary

    The aim of this chapter is first to set some basic notation and preliminaries (to be used through the book) and then recall the definition of affine Kac--Moody Lie algebras and their basic representation theory and to study the associated groups and their flag varieties. We define the loop group G((t)) (without the central extension) and its various subgroups. Then, we study the associated infinite Grassmannian and prove that it is a reduced ind-variety when G is a semisimple group. We show that G((t)) is a reduced affine ind-scheme. We further study the central extensions of G((t)).

  • The nominal/FM Yoneda Lemma

  • R. L. Crole
  • Journal:
    Mathematical Structures in Computer Science / Volume 30 / Issue 9 / October 2020
    Published online by Cambridge University Press:
    05 April 2021, pp. 1011-1024
    • Article
      • You have access
      • Open access
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  • This paper explores versions of the Yoneda Lemma in settings founded upon FM sets. In particular, we explore the lemma for three base categories: the category of nominal sets and equivariant functions; the category of nominal sets and all finitely supported functions, introduced in this paper; and the category of FM sets and finitely supported functions. We make this exploration in ordinary, enriched and internal settings. We also show that the finite support of Yoneda natural transformations is a theorem for free.

  • 1 - Basic Facts on Categories

  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book:
    Derived Categories
    Published online:
    15 November 2019
    Print publication:
    19 December 2019, pp 26-36

  • Summary

    This chapter is a brief review of standard material on categories and functors, including limits and the Yoneda Lemmas. A reader who is familiar with this material can skip this section, yet we recommend looking at our notational conventions, which are spelled out in Conventions 1.2.4 and 1.2.5.

  • Introduction

  • Radoslav Dimitric
  • Book:
    Slenderness
    Published online:
    30 November 2018
    Print publication:
    06 December 2018, pp 1-40

  • Summary

    This chapter contains the minimum of material needed to follow reasoning and constructions in subsequent chapters. Some new notions and research problems are also contained in this introductory chapter.