… -projective precover (resp. cover) of a left R-module M if and only if is an FP-projective precover
(… Dually we have the definitions of a ℬ-preenvelope and a ℬ-envelope (with the unique …

… functors in (mod-R, Ab) and n-strongly flat functors in ((mod-R)\(^{\text{ op }}\), Ab). In Section
3, we … precovers and preenvelopes by n-strongly FP-injective and n-strongly flat functors. In …

… of adjoint preenvelopes and adjoint precovers of functors. We … preenvelopes, adjoint precovers
and preenvelopes and … of these functors via the adjoint of preenvelopes and precovers. …

… , results about orthogonal classes and balanced functors in the category of complexes.
We … £precover. In a similar manner, we see that every object N of A has a special Çpreenvelope. …

… By using some results on perfect functor categories due to Harada and Simson [56], [83],
we then obtain that these perfectness conditions even characterize the existence of AddM-…

… the precovering classes that contain all the projective Rmodules. We first show that for such
a precovering … So an absolutely pure preenvelope of a module automatically gives us an …

… class of objects of a category C, by an F-precover of an object X … are those of an F-preenvelope
and F-envelope. When F is … by the pair (F, G) if the functor T (F,-) makes any complex 0→…

… a special CL-precover (resp., CLpreenvelope). As applications, … precover and a special
injective preenvelope, over a coherent ring every complex has a special FP-injective preenvelope…

… We show that if a class of modules is closed under pure quotients, then it is precovering if and
only … derived functors. Covering classes arise as a sharpening of the notion of precovering …

… special preenvelopes once we know special precovers exist and … that concrete classes are
special precovering or covering … a functor p from the product category s × S into the comma …