Foundations of Relative Homological Algebra
Samuel Eilenberg · J. C. Moore
Jan 1965 · American Mathematical Society: Memoirs of the American Mathematical Society Ibhuku elingu-55 · American Mathematical Soc.
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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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