# Homological Algebra

Princeton University Press, 1999 - Mathematics - 390 pages

When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied.

The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors."

This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

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### Contents

 II 3 III 18 IV 33 V 53 VI 75 VII 106 VIII 127 IX 143
 XIII 232 XIV 266 XV 289 XVI 315 XVII 340 XVIII 362 XIX 379 XX 387

 X 162 XI 182 XII 202

### References from web pages

Homological algebra - Wikipedia, the free encyclopedia
Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins ...
en.wikipedia.org/ wiki/ Homological_algebra

Geometry.Net - pure_and_applied_math: Homological Algebra
An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) by Charles A. Weibel, B. Bollobas, et all 27 October, 1995 ...
www5.geometry.net/ detail/ pure_and_applied_math/ homological_algebra.html

Homological algebra , by Henri Cartan and Samuel Eilenberg, The ...
Homological algebra deals both with the homology of algebraic systems and with. the algebraic aspects of homology theory. The first topic includes the ...
www.ams.org/ bull/ 2000-37-01/ S0273-0979-99-00837-X/ S0273-0979-99-00837-X.pdf

JSTOR: A Course in Homological Algebra.
A Course in Homological Algebra. By pj Hilton and U. Stammbach. Graduate Texts in Mathematics, Vol IV. Springer-Verlag, New York, 1971. ix + 338 pp. ...

Books on Homological Algebra
This was the first book on homological algebra I ever read, before I started graduate school. It is one of the most readable texts available, although some ...
www.math.hawaii.edu/ ~lee/ homolog/ books-homolog.html

Springer Online Reference Works
One of the origins of homological algebra is the (singular) homology theory of ... The language of homological algebra arose mainly from the process of ...
eom.springer.de/ H/ h047710.htm

18: Category theory, homological algebra
There are a number of textbooks on homological algebra which should be accessible to graduate ... Homological algebra, by Henri Cartan and Samuel Eilenberg. ...
www.math.niu.edu/ ~rusin/ known-math/ index/ 18-XX.html

Category theory in Homological Algebra
another context, namely homological algebra. During the creation and the ... What is homological algebra about? To put it simply, it is the study of alge- ...