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# CATEGORICAL PROPERTIES OF SEQUENTIALLY DENSE MONOMORPHISMS OF SEMIGROUP ACTS

05/1388;

ABSTRACT Let M be a class of (mono)morphisms in a category A. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair (A,M). In this paper we take A to be the category Act-S of S-acts, for a semigroup S, and M d to be the class of sequentially dense monomor-phisms (of interests to computer scientists, too) and study the categori-cal properties, such as limits and colimits, of the pair (A,M). Injectivity with respect to this class of monomorphisms have been studied by Giuli, Ebrahimi, and the authors and got information about injectivity relative to monomorphisms.

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Sep 23, 2013