‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...

‎‎‎In this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $S$-posets‎, ‎posets with a monotone action of a‎ pomonoid $S$ on them‎, ‎is studied‎. ‎We give a criterion‎, ‎like the Baer condition for injectivity of modules‎, ‎or Skornjakov criterion for injectivity of $S$-sets‎, ‎for the order dense injectivity‎. ‎Also‎, ‎we consider such injectivit...

‎for the subclasses ${mathcal m}_1$ and ${mathcal m}_2$ of‎‎monomorphisms in a concrete category $mathcal c$‎, ‎if ${mathcal‎‎m}_2subseteq {mathcal m}_1$‎, ‎then ${mathcal m}_1$-injectivity‎‎implies ${mathcal m}_2$-injectivity‎. ‎the baer type criterion is about‎ ‎the converse of this fact‎. ‎in this paper‎, ‎we apply injectivity to the classes of {it $c$-dense‎, ‎$c$-closed}‎ ‎monomorphisms‎. ...

It is known that injective Cellular Automata (CA) are surjective. In general, the converse is not true, and there are many algebraic CA counterexamples. However, there are interesting subclasses where this might be true. For example, if a surjective CA has entropy 0 then it is almost injective (Moothathu (2011)) and it is not known if it is actually injective. The author believes there are some...

Given a monad T on Set whose functor factors through the category of ordered sets with left adjoint maps, the category of Kleisli monoids is defined as the category of monoids in the hom-sets of the Kleisli category of T. The Eilenberg-Moore category of T is shown to be strictly monadic over the category of Kleisli monoids. If the Kleisli category of T moreover forms an order-enriched category,...

Given a group G of permutations of a finite n-element set Xn and a transformation f of Xn, the G-closure 〈f : G〉 of f is the semigroup generated by all the conjugates of f by permutations in G. A semigroup S of transformations of Xn is G-normal if GS = G, where GS consists of all the permutations h of Xn such that h−1fh ∈ S for all f ∈ S. We may assume that Xn is a chain and we let POIn be the ...

Let G and $$\Omega $$ be two planar domains. We give necessary sufficient conditions on a sequence $$(\phi _n)$$ of eventually injective holomorphic mappings from to for the existence function $$f\in H(\Omega )$$ whose orbit under composition by is dense in H(G). This extends result same nature obtained Grosse-Erdmann Mortini when $$G=\Omega . An interconnexion between topological properties ap...