@article {
author = {},
title = {Cover for Vol. 9, No. 1.},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {-},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {},
keywords = {},
url = {https://cgasa.sbu.ac.ir/article_65930.html},
eprint = {https://cgasa.sbu.ac.ir/article_65930_1e6b40c8fcf8398bfb33cedee74afaa6.pdf}
}
@article {
author = {Banaschewski, Bernhard and Hager, Anthony W.},
title = {Representation of $H$-closed monoreflections in archimedean $\ell$-groups with weak unit},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {1-13},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.1},
abstract = { The category of the title is called $\mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $\mathcal{A}$, $H\mathcal{A}$ consists of all homomorphic images of $\mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(\mathcal{R}, r)$ (meaning $H\mathcal{R} = \mathcal{R}$), about which we show ({\em inter alia}): $A \in \mathcal{A}$ if and only if $A$ is a countably up-directed union from $H\{rF(\omega)\}$. The meaning of this is then analyzed for two important cases: the maximum essential monoreflection $r = c^{3}$, where $c^{3}F(\omega) = C(\RR^{\omega})$, and $C \in H\{c(\RR^{\omega})\}$ means $C = C(T)$, for $T$ a closed subspace of $\RR^{\omega}$; the epicomplete, and maximum, monoreflection, $r = \beta$, where $\beta F(\omega) = B(\RR^{\omega})$, the Baire functions, and $E \in H\{B(\RR^{\omega})\}$ means $E$ is {\em an} epicompletion (not ``the'') of such a $C(T)$.},
keywords = {Archimedean $ell$-group,$H$-closed monoreflection,Yosida representation,countable composition,epicomplete,Baire functions},
url = {https://cgasa.sbu.ac.ir/article_61475.html},
eprint = {https://cgasa.sbu.ac.ir/article_61475_f777dd362fb1959c3a9aa5115a63f9a9.pdf}
}
@article {
author = {Ebrahimi Atani, Shahabaddin and Dolati Pishhesari, Saboura and Khoramdel, Mehdi and Sedghi, Maryam},
title = {Total graph of a $0$-distributive lattice},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {15-27},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.15},
abstract = {Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${\rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${\rm T}(G (£))$. It is the graph with all elements of £ as vertices, and for distinct $x, y \in £$, the vertices $x$ and $y$ are adjacent if and only if $x \vee y \in {\rm Z}(£)$. The basic properties of the graph ${\rm T}(G (£))$ and its subgraphs are studied. We investigate the properties of the total graph of $0$-distributive lattices as diameter, girth, clique number, radius, and the independence number.},
keywords = {Lattice,minimal prime ideal,zero-divisor graph,total graph},
url = {https://cgasa.sbu.ac.ir/article_50749.html},
eprint = {https://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdf}
}
@article {
author = {Lucatelli Nunes, Fernando},
title = {On lifting of biadjoints and lax algebras},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {29-58},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.29},
abstract = {Given a pseudomonad $\mathcal{T} $ on a $2$-category $\mathfrak{B} $, if a right biadjoint $\mathfrak{A}\to\mathfrak{B} $ has a lifting to the pseudoalgebras $\mathfrak{A}\to\mathsf{Ps}\textrm{-}\mathcal{T}\textrm{-}\mathsf{Alg} $ then this lifting is also right biadjoint provided that $\mathfrak{A} $ has codescent objects. In this paper, we give general results on lifting of biadjoints. As a consequence, we get a biadjoint triangle theorem which, in particular, allows us to study triangles involving the $2$-category of lax algebras, proving analogues of the result described above. In the context of lax algebras, denoting by $\ell :\mathsf{Lax}\textrm{-}\mathcal{T}\textrm{-}\mathsf{Alg} \to\mathsf{Lax}\textrm{-}\mathcal{T}\textrm{-}\mathsf{Alg} _\ell $ the inclusion, if $R: \mathfrak{A}\to\mathfrak{B} $ is right biadjoint and has a lifting $J: \mathfrak{A}\to \mathsf{Lax}\textrm{-}\mathcal{T}\textrm{-}\mathsf{Alg} $, then $\ell\circ J$ is right biadjoint as well provided that $\mathfrak{A} $ has some needed weighted bicolimits. In order to prove such result, we study descent objects and lax descent objects. At the last section, we study direct consequences of our theorems in the context of the $2$-monadic approach to coherence.},
keywords = {Lax algebras,pseudomonads,biadjunctions,adjoint triangles,lax descent objects,descent categories,weighted bi(co)limits},
url = {https://cgasa.sbu.ac.ir/article_50747.html},
eprint = {https://cgasa.sbu.ac.ir/article_50747_e7751692a69d525e49259ebe2763142f.pdf}
}
@article {
author = {Karimi Feizabadi, Abolghasem and Estaji, Ali Akbar and Robat Sarpoushi, Maryam},
title = {Pointfree topology version of image of real-valued continuous functions},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {59-75},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.59},
abstract = {Let $ { \mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree version of $C_c(X).$The main aim of this paper is to present the pointfree version of image of real-valued continuous functions in $ {\mathcal{R}} L$. In particular, we will introduce the pointfree version of the ring $C_c(X)$. We define a relation from $ {\mathcal{R}} L$ into the power set of $\mathbb R$, namely overlap . Fundamental properties of this relation are studied. The relation overlap is a pointfree version of the relation defined as $\mathop{\hbox{Im}} (f) \subseteq S$ for every continuous function $f:X\rightarrow\mathbb R$ and $ S \subseteq \mathbb R$.},
keywords = {frame,ring of real-valued continuous functions,countable image,$f$-ring},
url = {https://cgasa.sbu.ac.ir/article_50745.html},
eprint = {https://cgasa.sbu.ac.ir/article_50745_d90d55e08316779860740922b0388294.pdf}
}
@article {
author = {Hofmann, Dirk and D. Reis, Carla},
title = {Convergence and quantale-enriched categories},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {77-138},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.77},
abstract = {Generalising Nachbin's theory of ``topology and order'', in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\V$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category.},
keywords = {Ordered compact Hausdorff space,metric space,approach space,sober space,Cauchy completness,quantale-enriched category},
url = {https://cgasa.sbu.ac.ir/article_58262.html},
eprint = {https://cgasa.sbu.ac.ir/article_58262_bab8553989f148c1daf7939ffd5b9f4d.pdf}
}
@article {
author = {Borzooei, Rajabali and Hosseini, Fateme and Zahiri, Omid},
title = {Convex $L$-lattice subgroups in $L$-ordered groups},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {139-161},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.139},
abstract = {In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result about the set of all convex subgroups of a lattice ordered group and prove that $C(G)$, the set of all convex $L$-lattice subgroups of an $L$-ordered group $G$, is an $L$-complete lattice on height one. Then we use these objects to construct the quotient $L$-ordered groups and state some related results.},
keywords = {$L$-ordered group,convex $L$-subgroup,(normal) convex $L$-lattice subgroup},
url = {https://cgasa.sbu.ac.ir/article_50748.html},
eprint = {https://cgasa.sbu.ac.ir/article_50748_0ee3783313053dea8791d1990de4c8e2.pdf}
}
@article {
author = {},
title = {Persian Abstracts, Vol. 9, No. 1.},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {172-182},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {},
keywords = {},
url = {https://cgasa.sbu.ac.ir/article_65931.html},
eprint = {https://cgasa.sbu.ac.ir/article_65931_d0ea46be4127864d66630e8a8548674d.pdf}
}