Taiwanese Journal of Mathematics

Categorical Properties of Sequentially Dense Monomorphisms of Semigroup Acts

Mojgan Mahmoudi and Leila Shahbaz

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406220

Digital Object Identifier
doi:10.11650/twjm/1500406220

Mathematical Reviews number (MathSciNet)
MR2810167

Zentralblatt MATH identifier
1236.18003

Subjects
Primary: 08B25: Products, amalgamated products, and other kinds of limits and colimits [See also 18A30] 18A20: Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 18A30: Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 20M30: Representation of semigroups; actions of semigroups on sets 20M50: Connections of semigroups with homological algebra and category theory

Keywords
sequential closure sequential dense

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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