Geodesic
Notes on Several Orthogonal Classes of Flat and $FP$-injective Functors
Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 93-108

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In this paper, we develop relative homological algebra in the category of functors from finitely presented modules to Abelian groups. More specifically, we introduce the concepts of $\mathfrak{F}$-injective, $\mathfrak{F}$-projective and $\mathfrak{F}$-flat functors. Such functors appear when we study covers and envelopes of functors. The relationships among these functors are investigated and some applications are given.
Keywords: $\mathfrak{F}$-injective functor, $\mathfrak{F}$-projective functor, $\mathfrak{F}$-flat functor, $FP$-injective functor, flat functor, (pre)envelope, (pre)cover. 
@article{MZM_2014_95_1_a7,
     author = {Lixin Mao},
     title = {Notes on {Several} {Orthogonal} {Classes} of {Flat} and $FP$-injective {Functors}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {93--108},
     publisher = {mathdoc},
     volume = {95},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a7/}
}
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Lixin Mao. Notes on Several Orthogonal Classes of Flat and $FP$-injective Functors. Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 93-108. http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a7/