Definition of Derived Functors

Definition 2.1.1. A A-functor F J — E is right-derivable if there exists a A-functor 

Such a pair (RF, C) (respectively (LF, )) is called a right-derived (respectively left-derived) functor of F. 

Example 2.1.3. If F J — E transforms quasi-isomorphisms into isomorphisms then F = Fog for a unique F Dj — E and (F, identity) is both a right-derived and a left-derived functor of F. 

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