M. Mahmoudi
Department of Mathematics, Shahid Beheshti University, Tehran, Iran.
[ 1 ] - Subdirectly irreducible acts over some semigroups
In this paper, we characterize and find the number of subdirectly irreducible acts over some classes of semigroups, such as zero semigroups, right zero semigroups and strong chain of left zero semigroups.
[ 2 ] - The category of monoid actions in Cpo
In this paper, some categorical properties of the category ${bf Cpo}_{{bf Act}text{-}S}$ of all {cpo $S$-acts}, cpo's equipped with actions of a monoid $S$ on them, and strict continuous action-preserving maps between them is considered. In particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. Also, we show that the forgetful functor from...
[ 3 ] - Injectivity in a category: an overview on smallness conditions
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 boundedness, cogenerating set, and residual smallness. In this overview paper, we first try to refresh these smallness condition by giving the detailed proofs of the results mainly by Bernhard Banaschewski and W...
[ 4 ] - Separated finitely supported $Cb$-sets
The monoid $Cb$ of name substitutions and the notion of finitely supported $Cb$-sets introduced by Pitts as a generalization of nominal sets. A simple finitely supported $Cb$-set is a one point extension of a cyclic nominal set. The support map of a simple finitely supported $Cb$-set is an injective map. Also, for every two distinct elements of a simple finitely supported $Cb$-set, there exists...
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