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. The Category of Categories as a Foundation for Mathematics.- Fibred and Cofibred Categories.- Some Aspects of Equational Categories.- Representation in Abelian Categories.- Stable Homotopy.- Splitting Homotopy Idempotents.- Fill-in Theorems.- Coherent Functors.- Epimorphisms and Dominions.- Categories of Mapping Filters.- Correspondences and Exact Squares.- Canonical Categories.- Operational Categories.- Transparent Categories and Categories of Transition Systems.- A Homology Theory for Small Categories.- Acyclic Models and Triples.- Cohomology in Tensored Categories.- Extraordinary Homology and Chain Complexes.- Direct Decomposition of Radicals.- Abelian Extensions and a Cohomology Theory by Harrison.- Quotient Categories of Modules.- Closed Categories.
