In this paper we study the notion of injectivity in the category Pos-S of S-posets for a
pomonoid S. First we see that, although there is no non-trivial injective S-poset with respect …

Some of the so called smallness conditions in algebra as well as in category theory, are
important and interesting for their own and also tightly related to injectivity, are essential …

In this paper, some Baer type criteria are considered for locally presentable categories.
Recalling the notion of the classical Baer criterion for injectivity, it is shown that a locally …

A familiar construction for a Boolean algebra A is its normal completionN A, given by its
normal ideals or, equivalently, the intersections of its principal ideals, together with the …

Two important algebraic structures are S‐acts and Boolean algebras. Combining these two
structures, one gets S‐Boolean algebras, equipped with a compatible right action of a …

One of the aims of the modern representation theory is to solve classification problems for
subcategories of modules over a unitary ring R. In this paper, we introduce the concept of 1 …

In this paper we study topological spaces, frames, and their confrontation in the presheaf
topos of $ M $-sets for a monoid $ M $. We introduce the internalization, of the frame of open …

Injectivity (weakly injectivity) of objects is an important concept which category theory
inherited from homological and commutative algebra. One of the useful kinds of weakly …

It is well known that injective objects play a fundamental role in many branches of
mathematics. The question whether a given category has enough injective objects has been …

The famous Stone representation theorem for Boolean algebras represents them as
subalgebras of the powerset Boolean algebras. In this paper, we consider a Stone type …