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Foundations of relative homological algebra

Author: Samuel Eilenberg; John C Moore
Publisher: Providence, R.I. : American Mathematical Society, 1965.
Series: Memoirs of the American Mathematical Society, no. 55.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
The main notion of this paper is that of a "projective class of sequences" in an arbitrary (pointed) category. Each such class carries with it its own projective objects. One can then talk about projective resolutions, and if the category is additive, all the usual properties of the resolutions hold. In particular, this will permit the development of homological algebra in some additive categories which are not  Read more...
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Additional Physical Format: Online version:
Eilenberg, Samuel.
Foundations of relative homological algebra.
Providence, R.I. : American Mathematical Society, 1965
(OCoLC)654569091
Document Type: Book
All Authors / Contributors: Samuel Eilenberg; John C Moore
ISBN: 0821812556 9780821812556
OCLC Number: 1361982
Description: 39 pages : illustrations, diagrams ; 26 cm.
Contents: Introduction --
Relative homological algebra --
The adjoint theorem --
Examples --
Complexes in an abelian category.
Series Title: Memoirs of the American Mathematical Society, no. 55.
Responsibility: by Samuel Eilenberg and J.C. Moore.

Abstract:

The main notion of this paper is that of a "projective class of sequences" in an arbitrary (pointed) category. Each such class carries with it its own projective objects. One can then talk about projective resolutions, and if the category is additive, all the usual properties of the resolutions hold. In particular, this will permit the development of homological algebra in some additive categories which are not abelian, e.g., the category of comodules over a coalgebra over an arbitrary commutative ring.

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