Existence of Derived Functors

This applies in particular to the triangle (1.4.4.2) associated to an exact sequence of -complexes 

Derivability of a given functor is often proved by reduction, via suitable A-equivalences of categories, to the trivial example (2.1.3), as we now 

In either situation, j identifies D with a A-subcategory of D there is a A-functor p, 6) D — D with 

Proposition 2.2.3. With preceding notation, let E 6e o A-category, let F J — E be a A-functor, and suppose that the restricted functor 

A similar statement holds for left-derived functors when there exists a family as in (2.2). 

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