Algebra, Topology, and Category Theory

Algebra, Topology, and Category Theory

A Collection of Papers in Honor of Samuel Eilenberg

1st Edition - January 28, 1976

Write a review

  • Editors: Alex Heller, Myles Tierney
  • eBook ISBN: 9781483262611

Purchase options

Purchase options
DRM-free (PDF)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order


Algebra, Topology, and Category Theory: A Collection of Papers in Honor of Samuel Eilenberg is a collection of papers dealing with algebra, topology, and category theory in honor of Samuel Eilenberg. Topics covered range from large modules over artin algebras to two-dimensional Poincaré duality groups, along with the homology of certain H-spaces as group ring objects. Variable quantities and variable structures in topoi are also discussed. Comprised of 16 chapters, this book begins by looking at the relationship between the representation theories of finitely generated and large (not finitely generated) modules over an artin algebra. The reader is then introduced to reduced bar constructions on deRham complexes; some properties of two-dimensional Poincaré duality groups; and properties invariant within equivalence types of categories. Subsequent chapters explore the work of Samuel Eilenberg in topology; local complexity of finite semigroups; global dimension of ore extensions; and the spectrum of a ringed topos. This monograph will be a useful resource for students and practitioners of algebra and mathematics.

Table of Contents

  • List of Contributors


    Large Modules over Artin Algebras


    1. Preliminary Results

    2. Proof of Theorem A

    3. Proof of Theorem B


    Reduced Bar Constructions on deRham Complexes

    1. Bar Construction on DG Algebras

    2. The Eilenberg-Moore Spectral Sequence

    3. A Pairing of B(A) and a Cobar Construction

    4. The E1 Term of the Cobar Construction

    5. Applications


    Flatness and ProjectIvity of Modules That Come from ℂ-Sets

    1. Nonadditive Flatness

    2. Flatness of ℤM

    3. Nonadditive Projectivity

    4. Projectivity of ℤM


    Some Properties of Two-Dimensional Poincaré Duality Groups

    1. Preparatory Material

    2. Proof of Theorem A

    3. Proof of Theorem B

    4. The Pro-p-Completion of a Surface Group


    Properties Invariant within Equivalence Types of Categories

    1. The Diagrammatic Language

    2. The Theorem

    3. Back to Frege

    Coherence for the Tensor Product of 2-Categories, and Braid Groups


    1. The Tensor Product

    2. The N-Dimensional Cube QN as a 2-Category

    3. Proofs of the Lemmata


    Homology of Certain H-Spaces as Group Ring Objects

    1. Ring Objects

    2. Additive and Multiplicative Group Functors

    3. Existence of the Group Ring Functor

    4. Basic Classes of Examples of Group Rings

    5. The Group Ring H*+(Z x FΨq, k)

    6. The Group Rings H*(Z x BGL(Fq), k) and H*(Z x BGL(Fq), k)


    A Whitehead Theorem

    1. Introduction

    2. The Bousfield Factorization

    3. The Whitehead Theorem


    Variable Quantities and Variable Structures in Topoi





    The Work of Samuel Eilenberg in Topology


    What It Means for a Coalgebra To Be Simply Connected


    Local Complexity of Finite Semigroups

    1. Complexity Axioms

    2. Elementary and Type V Subsemigroups

    3. The Largest Local Complexity Function


    The Global Dimensions of Ore Extensions and Weyl Algebras


    1. Ore Extensions

    2. Weyl Algebras

    3. Examples


    Global Dimension of Ore Extensions

    1. Introduction

    2. Tor Functor and Intersections

    3. Ore Extensions

    4. The Commutative Case


    On the Spectrum of a Ringed Topos

    1. Localization, Primes, Local Rings, Etc.

    2. The Problem of the Spectrum and Some Previous Solutions

    3. A New Method


    Forcing Topologies and Classifying Topoi

    1. Forcing Topologies

    2. The Classifying Topos


    Published Works of Samuel Eilenberg

Product details

  • No. of pages: 238
  • Language: English
  • Copyright: © Academic Press 1976
  • Published: January 28, 1976
  • Imprint: Academic Press
  • eBook ISBN: 9781483262611

About the Editors

Alex Heller

Myles Tierney

Ratings and Reviews

Write a review

There are currently no reviews for "Algebra, Topology, and Category Theory"