Proceedings of the Conference on Categorical Algebra : La Jolla 1965

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. Front Matter....Pages i-viii The Category of Categories as a Foundation for Mathematics....Pages 1-20 Fibred and Cofibred Categories....Pages 21-83 Some Aspects of Equational Categories....Pages 84-94 Representations in Abelian Categories....Pages 95-120 Stable Homotopy....Pages 121-172 Splitting Homotopy Idempotents....Pages 173-176 Fill-in Theorems....Pages 177-188 Coherent Functors....Pages 189-231 Epimorphisms and Dominions....Pages 232-246 Categories of Mapping Filters....Pages 247-253 Correspondences and Exact Squares....Pages 254-271 Canonical Categories....Pages 272-294 Operational Categories....Pages 295-316 Transparent Categories and Categories of Transition Systems....Pages 317-330 A Homology Theory for Small Categories....Pages 331-335 Acyclic Models and Triples....Pages 336-343 Cohomology in Tensored Categories....Pages 344-354 Extraordinary Homology and Chain Complexes....Pages 355-365 Direct Decompositions of Radicals....Pages 366-374 Abelian Extensions and a Cohomology Theory of Harrison....Pages 375-403 Quotient Categories of Modules....Pages 404-420 Closed Categories....Pages 421-562