Algebra, Topology, and Category Theory

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