… on the notions of precovers and preenvelopes. Recall that a … ] studied ideal cotorsion pairs
in extension closed subcategories of … We recall that phantom morphisms were introduced by …

… Cotorsion pairs have been used to study precovers and preenvelopes (approximation theory…
-extension of morphisms. Using this concept, they proved an analog of Christensen’s Ghost …

… Meantime, they established the connection between special precovering ideals and phantom
… ⊥J -precover of A. The special J -preenvelope j : K → C arises from a pullback along a …

… We relate partial morphisms with (co-)phantom morphisms … in certain abelian categories
this preenvelopes can be used to … of special c-preenvelopes (a special b-precover of a module …

… Herzog studied phantom covers of modules by analyzing the functor … precovers with
preenvelopes. Recall that for a subcategory F of A, a map f : F → M is said to be an F-precover of M if …

… Since E -phantoms are saturated (Remark 3.4), we deduce … ( E ) -precovers and inj ( E )
-preenvelopes as being the correct … K of a chosen inj ( E ) -preenvelope X → X E . One can show …

… and Φ is the ideal of phantom morphisms in the category k[G]-… I-precover (respectively, I-preenvelope)
An ideal I is special … extension closed subcategory A of a triangulated category T . …

… extensions or extension-… precovers and preenvelopes exist under suitable finiteness
conditions on the category. In large silting theory, the existence of precovers and preenvelopes is …

… f : F → M with F ∈ F, is an F-precover if for any g: F′ → M with F′ ∈ F there is a map α:
F′ → F such that g = fα. If f : F → M is an F-precover, we say it is an F-cover if for any α: F → F …

… σpΦq is an H0 σpS q-preenvelope of H0 σpσq, we also have … Since γ1 is an extension of
σr1s (which lies in Yr1s Ď Y1) and … S -precovers are S -precovers, we note that if σ admits an S -…