Algebra, Topology, and Category Theory
A Collection of Papers in Honor of Samuel Eilenberg
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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
Preface
Large Modules over Artin Algebras
Introduction
1. Preliminary Results
2. Proof of Theorem A
3. Proof of Theorem B
References
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
References
Flatness and ProjectIvity of Modules That Come from ℂ-Sets
1. Nonadditive Flatness
2. Flatness of ℤM
3. Nonadditive Projectivity
4. Projectivity of ℤM
References
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
References
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
Introduction
1. The Tensor Product
2. The N-Dimensional Cube QN as a 2-Category
3. Proofs of the Lemmata
References
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)
References
A Whitehead Theorem
1. Introduction
2. The Bousfield Factorization
3. The Whitehead Theorem
References
Variable Quantities and Variable Structures in Topoi
1.
2.
3.
References
The Work of Samuel Eilenberg in Topology
Bibliography
What It Means for a Coalgebra To Be Simply Connected
References
Local Complexity of Finite Semigroups
1. Complexity Axioms
2. Elementary and Type V Subsemigroups
3. The Largest Local Complexity Function
References
The Global Dimensions of Ore Extensions and Weyl Algebras
Introduction
1. Ore Extensions
2. Weyl Algebras
3. Examples
References
Global Dimension of Ore Extensions
1. Introduction
2. Tor Functor and Intersections
3. Ore Extensions
4. The Commutative Case
References
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
References
Forcing Topologies and Classifying Topoi
1. Forcing Topologies
2. The Classifying Topos
References
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
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