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Research and Exposition in Mathematics -- Volume 18

H. Herrlich and H.-E. Porst (eds.)

Category Theory at Work

410 pages, electronic publication, ISBN 3-88538-218-0, 1990

The purpose of this book is to serve as a text for a seminar in applied Category Theory. The treatise contains 23 articles, which are intended to paradigmatically demonstrate how categorical thinking contributes to a better understanding of certain mathematical phenomena by putting them into particularly suitable contexts. The papers discuss topics from Topology, Algebra, Computer Science, and Analysis.


vii--viii [FullText]

Section I: Topology

H. L. Bentley, H. Herrlich, R. Lowen
Improving Constructions in Topology
3--20 [FullText]

H. Herrlich, E. Lowen-Colebunders, F. Schwarz
Improving Top: PrTop and PsTop
21--34 [FullText]

F. Schwarz, S. Weck-Schwarz
Internal Description of Hulls: A Unified Approach
35--45 [FullText]

G. Preuss
Point Separation Axioms, Monotopological Categories and MacNeille Completions
47--55 [FullText]

M. Erné
The ABC of Order and Topology
57--83 [FullText]

P. T. Johnstone
The Art of Pointless Thinking: A Student's Guide to the Category of Locales
85--107 [FullText]

Section II: Topology Meets Algebra

H.-E. Porst, W. Tholen
Concrete Dualities
111-136 [FullText]

H. Herrlich, T. Mossakowski, G. E. Strecker
Algebra Union Topology
137--148 [FullText]

G. Jarzembski
Free Spectra of Concrete Categories and Mixed Structures
149--164 [FullText]

H.-E. Porst
On the Existence and Structure of Free Topological Groups
165--176 [FullText]

K. H. Hofmann, S. A. Morris
Free Compact Groups V: Remarks and Projectivity
177--198 [FullText]

G. Richter
Axiomatizing the Category of Compact Hausdorff Spaces
199--215 [FullText]

E. Makai jun.
Automorphisms and Full Embeddings of Categories in Algebra and Topology
217--260 [FullText]

G. Richter
Algebra Contained in Topology ?!
261--273 [FullText]

Section III: Algebra and Computer Science

J. Reiterman, V. Trnková
Free Structures
277--288 [FullText]

H. W. Bargenda
Universal Algebraic Completions of Right Adjoint Functors
289--306 [FullText]

M. Sobral
Contravariant Hom-Functors and Monadicity
307--319 [FullText]

H. Roehrl
Convexity Theories Upside-Down-Omega -- Back to the Future
321--324 [FullText]

J. W. Gray
Products in Per: An Elementary Treatment of the Semantics of the Polymorphic Lambda Calculus
325--340 [FullText]

Section IV: Analysis

L. D. Nel
Nonlinear Existence Theorems in Nonnormable Analysis
343--365 [FullText]

R. Boerger
Fubini's Theorem from a Categorical Viewpoint
367--375 [FullText]

Sophus Lie's Fundamental Theorem -- Categorical Aspects
377--386 [FullText]

D. Pumpluen, H. Roehrl
Convexity Theories II. The Hahn-Banach Theorem for Real Convexity Theories
387--395 [FullText]