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A Course in Homological Algebra

A Course in Homological Algebra
Catalogue Information
Field name Details
Dewey Class 512
Title A Course in Homological Algebra ([EBook]) / by P. J. Hilton, U. Stammbach.
Author Hilton, Peter John
Added Personal Name Stammbach, Urs
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer , 1971.
Physical Details IX, 340 p. 1 illus. : online resource.
Series Graduate texts in mathematics 0072-5285 ; ; 4
ISBN 9781468499360
Summary Note In this chapter we are largely influenced in our choice of material by the demands of the rest of the book. However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I. Of course the reader thoroughly familiar with category theory could, in principal, omit Chapter II, except perhaps to familiarize himself with the notations employed. In Chapter III we begin the proper study of homological algebra by looking in particular at the group ExtA(A, B), where A and Bare A-modules. It is shown how this group can be calculated by means of a projective presentation of A, or an injective presentation of B; and how it may also be identified with the group of equivalence classes of extensions of the quotient module A by the submodule B.:
Contents note I. Modules -- II. Categories and Functors -- III. Extensions of Modules -- IV. Derived Functors -- V. The Künneth Formula -- VI. Cohomology of Groups -- VII. Cohomology of Lie Algebras -- VIII. Exact Couples and Spectral Sequences -- IX. Satellites and Homology.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-1-4684-9936-0
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