Topology and Logic as a Source of Algebra S M Lane article英文电子书.pdf

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 82, Number 1, January 1976 TOPOLOGY AND LOGIC AS A SOURCE OF ALGEBRA Retiring Presidential Address1 BY SAUNDER S MA C LAN E Table of Contents Introduction 1 1: Separable extensions 1 2: Homological algebra 5 3 : The cohomology of groups 8 4: The bar construction 17 5: Coherence and canonical maps 24 6: Naturality and categories 33 7: What is algebra? 36 Introduction. Each President of the American Mathematical Society is required to present a retiring presidential address. By custom, this address is not in any way directed to the examination of the administrative or profes- sional problems of the Society. This is not because these problems are unimportant, but is presumably because the Presidents contribution to them should have long since been made, or not made, as the case may be, well before his retirement from office. Instead the custom is that the Presidents address is concerned with contributions to our science. This is a good custom, since it is the mathematical theorems and the