… We show for example that SM being coherent entails the existence of AddM-preenvelopes
for all finitely presented right R-modules. We also investigate some stronger coherence …

… the concepts of adjoint preenvelopes and adjoint precovers of modules and some … relationships
between adjoint preenvelopes, adjoint precovers and preenvelopes and precovers were …

… Moreover, if the only such g are automorphisms of F when F = F and f = φ, then the D-preenvelope
φ is called a D-envelope of M. Dually we have the notions of a D-precover and a D-…

… Also we define a new tensor product in the category of complexes which is left adjoint of
the … £precover. In a similar manner, we see that every object N of A has a special Çpreenvelope. …

… -precover, an Ω-cover and a special Ω-precover … module is Gorenstein projective, so it is
natural to ask whether every complex of left R-modules has a special DG-projective preenvelope…

… So by Lemma 2.3(ii) and Theorem 3.2, a homomorphism f : A → C in Mod R with C absolutely
pure is an absolutely pure preenvelope of A provided f + : C+ → A+ is a flat precover of A+ …

… that the class of Gorenstein flat modules is precovering over any rings. For Gorenstein projective
precovers, Jørgensen [19] proved … But this would follows from the adjoint isomorphism: …

… Precovers, covers, pre-envelopes and envelopes are often … So, for example, a flat cover
in the category of left R-modules … O(U)-module (this is just the typical adjoint procedure for …

… -right-assignment for C is a choice of -pre-envelopes for all objects of C. When a choice has
been made, the cokernel … In particular, I will soon find myself searching for a left-adjoint to Z0. …

… functor), and we let St : A/T → A be the fully faithful right adjoint of Qt. If A = Mod-R is the
category of right R-modules over a ring R, then we can consider the ring of quotients ψ : R → Rt …