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Memoirs of the American Mathematical Society 1965 No. 55 Foundations of Relative Homological Algebra

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Author(s): Samuel Eilenberg, J. C. Moore
Series: Mem.AMS-55
Publisher: American Mathematical Society
Year: 1965

Language: English
Pages: 40

Foundations of Relative Homological Algebra......Page 1
Introduction......Page 2
1. Review of categories......Page 3
2. Closed and projective classes......Page 6
3. Resolutions and derived functors......Page 7
4. Categories with kernels......Page 8
6. Resolvents......Page 10
1. Adjoint functors......Page 13
2. The adjoint theorem......Page 15
3. The multiple adjoint theorem......Page 17
4. A refinement......Page 18
5. Generators......Page 20
1. Groups......Page 21
2. Abelian groups......Page 23
3. Banach spaces......Page 25
4. Rings and modules......Page 27
5. Coalgebras, comodules and contramodules......Page 28
1. The category CA......Page 29
2. A general theorem......Page 33
3. Projective classes in CA......Page 34
4. Subcategories of CA......Page 36
5. An application......Page 38
Bibliography......Page 40