Proceedings of the Conference on Categorical Algebra

1. Front Matter

   Pages i-viii

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2. The Category of Categories as a Foundation for Mathematics

   • F. William Lawvere

   Pages 1-20

3. Fibred and Cofibred Categories

   • John W. Gray

   Pages 21-83

4. Some Aspects of Equational Categories

   • F. E. J. Linton

   Pages 84-94

5. Representations in Abelian Categories

   • Peter Freyd

   Pages 95-120

6. Stable Homotopy

   • Peter Freyd

   Pages 121-172

7. Splitting Homotopy Idempotents

   • Peter Freyd

   Pages 173-176

8. Fill-in Theorems

   • Richard Faber, Peter Freyd

   Pages 177-188

9. Coherent Functors

   • Maurice Auslander

   Pages 189-231

10. Epimorphisms and Dominions

    • John R. Isbell

    Pages 232-246

11. Categories of Mapping Filters

    • Erwin Engeler

    Pages 247-253

12. Correspondences and Exact Squares

    • Peter Hilton

    Pages 254-271

13. Canonical Categories

    • Johann Sonner

    Pages 272-294

14. Operational Categories

    • Oswald Wyler

    Pages 295-316

15. Transparent Categories and Categories of Transition Systems

    • Yehoshafat Give’on

    Pages 317-330

16. A Homology Theory for Small Categories

    • Charles E. Watts

    Pages 331-335

17. Acyclic Models and Triples

    • Michael Barr, Jon Beck

    Pages 336-343

18. Cohomology in Tensored Categories

    • Michael Barr

    Pages 344-354

19. Extraordinary Homology and Chain Complexes

    • Alex Heller

    Pages 355-365

20. Direct Decompositions of Radicals

    • Spencer Dickson

    Pages 366-374

This volume contains the articles contributed to the Conference on Categorical Algebra, held June 7-12,1965, at the San Diego campus of the University of California under the sponsorship of the United States Air Force Office of Scientific Research. Of the thirty-seven mathemati­ cians, who were present seventeen presented their papers in the form of lectures. In addition, this volume contains papers contributed by other attending participants as well as by those who, after having planned to attend, were unable to do so. The editors hope to have achieved a representative, if incomplete, cover­ age of the present activities in Categorical Algebra within the United States by bringing together this group of mathematicians and by solici­ ting the articles contained in this volume. They also hope that these Proceedings indicate the trend of research in Categorical Algebra in this country. In conclusion, the editors wish to thank the participants and contrib. utors to these Proceedings for their continuous cooperation and encour­ agement. Our thanks are also due to the Springer-Verlag for publishing these Proceedings in a surprisingly short time after receiving the manu­ scripts.

• Morphism
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• Columbia University, New York 27, USA

  S. Eilenberg

• Department of Mathematics, University of Oregon, Eugene, USA

  D. K. Harrison

• Department of Mathematics, The University of Chicago, Chicago, USA

  S. MacLane

• Department of Mathematics, University of California, San Diego, La Jolla, USA

  H. Röhrl

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