… relative to Ext. The first is a very general and elegant way to prove the existence of covers
with … In this way we establish the existence of pure injective envelopes of complexes and we …

… ⊥ contains all injective right R-modules, we have that Ncovers are epic and N … In this
section, first, we will remind certain relative injectivity conditions. Subsequently, we shall examine …

… cover and its facial submanifolds. In particular, we can determine when a facial submanifold
of a small cover is |$\pi _1$|-injective … _1$|-injectivity of a facial submanifold in a small cover: …

… of injective cover as the dual notation of the injective envelope… every right R-module has an
injective cover. In Section 3, we … In this case, B is injective and A is injective relative to B. Thus…

… injective resolutions in the category of OX -modules. This gives the same result as computing
local cohomology using injective … To do so, we establish a covering lemma in §6.1. We then …

… and projective relative to … covering and enveloping properties of min-pure injective and
minpure projective modules. We show that all min-pure injective modules have an injective cover, …

… We attach a relative theory of Gorenstein homological algebra to any given semi-complete …
The main application is that the Ding injective modules are the right side of a complete (perfect…

… of 𝑋, where we get an fpqc cover of a field, hence an ind-fppf cover (along which etale sheaves
… Now we check the injectivity in part (iii) of Lemma 5.5, so we can now assume that 𝑋 is …

… A ring R is said to be left m-injective if R is m-injective as a left R-module [10]. m-injective …
Since L has a monic m-injective cover φ : F → L by (3), there is α : E → F such that π = φα. Thus …

… -covers to study integer matrices. We show that the coefficient of any given minor is the
signed sum of restricted cycle-cover … set” is a functor into Set relative to each category. The set …