Abstract
Let $\mathcal M$ be a class of (mono)morphisms in a category $\mathcal A$. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair $(\mathcal{A},\mathcal{M})$. In this paper we take $\mathcal A$ to be the category Act-S of acts over a semigroup $S$, and ${\mathcal M}_d$ to be the class of sequentially dense monomorphisms (of interest to computer scientists, too) and study the categorical properties, such as limits and colimits, of the pair $(\mathcal{A},\mathcal{M})$. Injectivity with respect to this class of monomorphisms have been studied by Giuli, Ebrahimi, and the authors who used it to obtain information about injectivity relative to monomorphisms.
Citation
Mojgan Mahmoudi. Leila Shahbaz. "Categorical Properties of Sequentially Dense Monomorphisms of Semigroup Acts." Taiwanese J. Math. 15 (2) 543 - 557, 2011. https://doi.org/10.11650/twjm/1500406220
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