… Let R be a commutative ring and C a semidualizing R-module… injective (flat) modules
by introducing the concepts of n-C-… -C-copure flat modules and n-C-copure injective (projective) …

… We show that they are part of weak AB-contexts. As the … for formally inverting the weak
equivalences. We refer the reader to [… coincide with the concepts of C-flat and C-injective modules, …

… In Section 4, we investigate Foxby equivalence relative to C-FP n -injective and C-FP n -flat
modules. We also show that the class … C-FP ∞ -flat) if and only if M is C-weak injective (resp. …

… module” is a central notion in relative homological algebra. This notion was first introduced
by Foxby [9]. … , in which case condition (i) is equivalent to C being finitely generated. An R-…

… of (weak) flat modules, projective modules and AC (S) … the relation between the T -projective
dimension of HomR(C, M… of Mod R consisting of weak injective modules, and write …

… the Foxby equivalences associate to (V, W, Y, X)-Gorenstein … C = S, then we have a notion
of Gorenstein weak injective S-… In this section, we will study the Foxby equivalences relative …

… AB-context and weak AB-context have been studied by many people, see [4, 18, 29, 34, 35,
… sequence for any injective R-module I. An R-module M is C-Gorenstein flat if there exists a …

… the exact complexes of injective modules that remain exact … preenvelopes with respect to
these classes of modules has … cofibrations, fibrations, and weak equivalences, all subject to a …

… (R) and C(R) to denote the classes of injective, projective, flat … In the case n = 0, we obtain
other equivalent assertions … We also note that every right coherent ring is right weak coherent, …

… with C-Gorenstein projective, flat and injective modules and … It is well known that the weak
global dimension of any ring R … We may refer to modules in Foxby classes AC and BC as AC-…