Our aim is to give a fairly complete account on the construction of compatible model
structures on exact categories and symmetric monoidal exact categories, in some cases …

We put a monoidal model category structure on the category of chain complexes of quasi-
coherent sheaves over a quasi-compact and semi-separated scheme X. The approach …

A full subcategory of a Grothendieck category is called deconstructible if it consists of all
transfinite extensions of some set of objects. This concept provides a handy framework for …

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves on a semi-
separated noetherian scheme, and study these complexes using the pure derived category …

Let (A; E) be an exact category and F⊆ Ext a subfunctor. A morphism φ in A is an F-phantom
if the pullback of an E-conflation along φ is a conflation in F. If the exact category (A; E) has …

We show that in a finitely accessible additive category every class of objects closed under
direct limits and pure epimorphic images is covering. In particular, the classes of flat objects …

In this paper we develop a general theory of modules which are invariant under
automorphisms of their covers and envelopes. When applied to specific cases like injective …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …

If R is an associative ring with identity, a theory of minimal flat resolutions is developed in the
category ((R-mod) op, Ab) of contravariant functors G:(R-mod) op→ Ab from the category R …

PURE-INJECTIVE ENVELOPES Page 1 November 5, 2003 12:16 WSPC/171-JAA 00058
Journal of Algebra and Its Applications Vol. 2, No. 4 (2003) 397–402 c© World Scientific …