Heller / Tierney Algebra, Topology, and Category Theory

A Collection of Papers in Honor of Samuel Eilenberg
1. Auflage 2014
ISBN: 978-1-4832-6261-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 238 Seiten, Web PDF

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.

Autoren/Hrsg.

Heller, Alex

Tierney, Myles

Inhaltsverzeichnis

1;Front Cover
;1
2;Algebra, Topology, and Category Theory: A Collection of Papers in Honor of Samuel Eilenberg;4
3;Copyright Page;5
4;Table of Contents;6
5;List of Contributors;10
6;Preface;12
7;Chapter 1.
Large Modules over Artin Algebras;14
7.1;Introduction;14
7.2;1. Preliminary Results;15
7.3;2. Proof of Theorem A;20
7.4;3. Proof of Theorem B;25
7.5;References;29
8;Chapter 2.
Reduced Bar Constructions on deRham Complexes;32
8.1;1. Bar Construction on DG Algebras;33
8.2;2. The Eilenberg–Moore Spectral Sequence;36
8.3;3. A Pairing of B(A) and a Cobar Construction;38
8.4;4. The E1 Term of the Cobar Construction;40
8.5;5. Applications;42
8.6;References;44
9;Chapter 3.
Flatness and Project!vity of Modules That Come from C-Sets;46
9.1;1. Nonadditive Flatness;47
9.2;2. Flatness of ZM;48
9.3;3. Nonadditive Projectivity;52
9.4;4. Projectivity of ZM;53
9.5;References;57
10;Chapter 4. Some Properties of Two-Dimensional Poincaré Duality Groups;58
10.1;1. Preparatory Material;59
10.2;2. Proof of Theorem A;62
10.3;3. Proof of Theorem B;63
10.4;4. The Pro-p-Completion of a Surface Group;65
10.5;References;66
11;Chapter 5.
Properties Invariant within Equivalence Types of Categories;68
11.1;1. The Diagrammatic Language;69
11.2;2. The Theorem;72
11.3;3. Back to Frege;73
12;Chapter 6.
Coherence for the Tensor Product of 2-Categories, and Braid Groups;76
12.1;Introduction;76
12.2;1. The Tensor Product;77
12.3;2. The JV-Dimensional Cube QN as a 2-Category;81
12.4;3. Proofs of the Lemmata;84
12.5;References;88
13;Chapter 7.
Homology of Certain H-Spaces as Group Ring Objects;90
13.1;1. Ring Objects;91
13.2;2. Additive and Multiplicative Group Functors;94
13.3;3. Existence of the Group Ring Functor;96
13.4;4. Basic Classes of Examples of Group Rings;100
13.5;5. The Group Ring H* (Z x F.q, k);102
13.6;6. The Group Rings H* (Z x BGL(Fq), k) and H*(Z x BGL(Fq), k);105
13.7;References;107
14;Chapter 8.
A Whitehead Theorem;108
14.1;1. Introduction;108
14.2;2. The Bousfield Factorization;109
14.3;3. The Whitehead Theorem;110
14.4;References;112
15;Chapter 9.
Variable Quantities and Variable Structures in Topoi;114
15.1;1;115
15.2;2;131
15.3;3;141
15.4;References;144
16;Chapter 10.
The Work of Samuel Eilenberg in Topology;146
16.1;Bibliography;155
17;Chapter 11.
What It Means for a Coalgebra To Be Simply Connected;158
17.1;References;161
18;Chapter 12. Local Complexity of Finite Semigroups;162
18.1;1. Complexity Axioms;162
18.2;2. Elementary and Type V Subsemigroups;166
18.3;3. The Largest Local Complexity Function;172
18.4;References;180
19;Chapter 13.
The Global Dimensions of Ore Extensions and Weyl Algebras;182
19.1;Introduction;182
19.2;1. Ore Extensions;183
19.3;2. Weyl Algebras;186
19.4;3. Examples;191
19.5;References;192
20;Chapter 14.
Global Dimension of Ore Extensions;194
20.1;1. Introduction;194
20.2;2. Tor Functor and Intersections;195
20.3;3. Ore Extensions;196
20.4;4. The Commutative Case;199
20.5;References;200
21;Chapter 15.
On the Spectrum of a Ringed Topos;202
21.1;1. Localization, Primes, Local Rings, Etc;203
21.2;2. The Problem of the Spectrum and Some Previous Solutions;209
21.3;3. A New Method;216
21.4;References;223
22;Chapter 16.
Forcing Topologies and Classifying Topoi;224
22.1;1. Forcing Topologies;225
22.2;2. The Classifying Topos;227
22.3;References;232
23;Published Works of Samuel Eilenberg;234