## Taiwanese Journal of Mathematics

### Categorical Properties of Sequentially Dense Monomorphisms of Semigroup Acts

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 2 (2011), 543-557.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406220

Digital Object Identifier
doi:10.11650/twjm/1500406220

Mathematical Reviews number (MathSciNet)
MR2810167

Zentralblatt MATH identifier
1236.18003

#### Citation

Mahmoudi, Mojgan; Shahbaz, Leila. Categorical Properties of Sequentially Dense Monomorphisms of Semigroup Acts. Taiwanese J. Math. 15 (2011), no. 2, 543--557. doi:10.11650/twjm/1500406220. https://projecteuclid.org/euclid.twjm/1500406220

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