If a posets lacks joins of directed subsets, one can pass to its ideal completion. But doing this means also changing the setting: The universal property of ideal completion of posets suggests that it should be regarded as a functor from the category of posets with monotone maps to the category of dcpos with Scott-continuous functions as morphisms. The same applies for the quantitative version ...

The purpose of this paper is to establish injectivity theorems for higher direct image sheaves canonical bundles twisted by pseudo-effective line and multiplier ideal sheaves. As applications, we generalize Koll'ar's torsion freeness Grauert-Riemenschneider's vanishing theorem. Moreover, obtain a relative theorem Kawamata-Viehweg-Nadel type an extension holomorphic sections from fibers morphism...

We present a setting for the study of torsion theories in general categories. The idea is to associate, with any pair ($\mathcal T$, $\mathcal F$) full replete subcategories category C$, corresponding subcategory Z = \mathcal T \cap F$ \emph{trivial objects} C$. morphisms which factor through Z$ are called Z$-trivial, and these form an ideal morphisms, respect one can define Z$-prekernels, Z$-p...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.

‎In this paper‎, ‎we prove that the category of crossed polymodules (i.e‎. ‎crossed modules of polygroups) and their morphisms is finitely complete‎. ‎We‎, ‎therefore‎, ‎generalize the group theoretical case of this completeness property of crossed modules‎.