<p>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.</p>

A Course in Homological Algebra (Graduate Texts in Mathematics)

Science & Math

P.J. Hilton and Urs Stammbach

Mathematics

Springer

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Books by P.J. Hilton and Urs Stammbach

See the best price to sell, buy, or rent books by P.J. Hilton and Urs Stammbach. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

A Course in Homological Algebra (Graduate Texts in Mathematics)