Algebra, Topology, and Category Theory : A Collection of Papers in Honor of Samuel Eilenberg

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. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv List of Contributors, Pages ix-x Preface, Page xi Large Modules over Artin Algebras, Pages 1-17, MAURICE AUSLANDER Reduced Bar Constructions on deRham Complexes, Pages 19-32, KUO-TSAI CHEN Flatness and Projectivity of Modules That Come from C-Sets, Pages 33-44, CHARLES CHING-AN CHENG, BARRY MITCHELL Some Properties of Two-Dimensional Poincaré Duality Groups, Pages 45-54, ELDON DYER, A.T. VASQUEZ Properties Invariant within Equivalence Types of Categories, Pages 55-61, PETER FREYD Coherence for the Tensor Product of 2-Categories, and Braid Groups, Pages 63-76, JOHN W. GRAY Homology of Certain H-Spaces as Group Ring Objects, Pages 77-94, DALE HUSEMOLLER A Whitehead Theorem, Pages 95-99, D.M. KAN Variable Quantities and Variable Structures in Topoi, Pages 101-131, F. WILLIAM LAWVERE The Work of Samuel Eilenberg in Topology, Pages 133-144, SAUNDERS MAC LANE What It Means for a Coalgebra To Be Simply Connected, Pages 145-148, JOHN C. MOORE Local Complexity of Finite Semigroups, Pages 149-168, JOHN RHODES, BRET TILSON The Global Dimensions of Ore Extensions and Weyl Algebras, Pages 169-180, GEORGE S. RINEHART, ALEX ROSENBERG Global Dimension of Ore Extensions, Pages 181-188, ALEX ROSENBERG, J.T. STAFFORD On the Spectrum of a Ringed Topos, Pages 189-210, MYLES TIERNEY Forcing Topologies and Classifying Topoi, Pages 211-219, MYLES TIERNEY Published Works of Samuel Eilenberg, Pages 221-225 Auslander, M. Large Modules Over Artin Algebras. -- Chen, K.-t. Reduced Bar Constructions On Derham Complexes. -- Cheng, C.c., And Mitchell, B. Flatness And Projectivity Of Modules That Come From C-sets. -- Dyer, E., And Vasquez. A.t. Some Properties Of Two-dimensional Poincaré Duality Groups. -- Freyd, P. Properties Invariant Within Equivalence Types Of Categories. -- Gray, J.w. Coherence For The Tensor Product Of 2-categories, And Braid Groups. -- Husemoller, D. Homology Of Certain H-spaces As Group Ring Objects. -- Kan, D.m.a Whitehead Theorem. -- Lawvere, F.w. Variable Quantities And Variable Structures In Topoi. -- Mac Lane, S. The Work Of Samuel Eilenberg In Topology. -- Moore, J.c. What It Means For A Coalgebra To Be Simply Connected. -- Rhodes, J., And Tilson, B. Local Complexity Of Finite Semigroups. -- Rinehart, G.s., And Rosenberg, A. The Global Dimension Of Ore Extensions And Weyl Algebras. -- Rosenberg, A., And Stafford, J.t. Global Dimension Of Ore Extensions. -- Tierney, M. On The Spectrum Of A Ringed Topos. -- Tierney, M. Forcing Topologies And Classifying Topoi. Edited By Alex Heller, Myles Tierney. Many Of These Papers ... Were Read At A Conference Held May 3 And 4, 1974, On The Occasion Of Professor Eilenberg's Sixtieth Birthday, At The Graduate Center Of The City University Of New York. Published Works Of Samuel Eilenberg: P. 221-225. Includes Bibliographies.