## Foundations of relative homological algebra |

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6-projective A-module abelian category abelian groups additive categories additive functor adjoint theorem adjointness relation Banach space base point bijection biproduct category Q category with kernels Chapter class in Q class of sequences closed class coadjoint coexact cokernel commutative diagram comodules Consider the functor coproducts of copies cyclic groups De(f denote derived functors Dk(f double complex exact projective class exists a morphism faithful finite number fl(P following properties follows from 2.1 free group full subcategory given implies injective class injectively perfect isomorphism left complex let Q LS(B modules monomorphism morphism f morphisms in SB normal Cİ-subcategory normal subcategory pair F phisms pre-additive category preserves epimorphisms projective objects projective resolution projectively perfect Proof properties are equivalent Proposition 1.1 Q and let RELATIVE HOMOLOGICAL ALGEBRA resolvent pair retracts of coproducts satisfying spectral sequence split exact sequences strongly exact surjective Theorem 2.1 tive objects trivial objects unique morphism