2020-07-07T06:24:41Z
http://cgasa.sbu.ac.ir/?_action=export&rf=summon&issue=8377
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
9
1
Cover for Vol. 9, No. 1.
2018
07
01
http://cgasa.sbu.ac.ir/article_65930_1e6b40c8fcf8398bfb33cedee74afaa6.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
9
1
Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit
Bernhard
Banaschewski
Anthony W.
Hager
The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), 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 $C(T)$.
Archimedean $ell$-group
$H$-closed monoreflection
Yosida representation
countable composition
epicomplete
Baire functions
2018
07
01
1
13
http://cgasa.sbu.ac.ir/article_61475_f777dd362fb1959c3a9aa5115a63f9a9.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
9
1
Total graph of a $0$-distributive lattice
Shahabaddin
Ebrahimi Atani
Saboura
Dolati Pishhesari
Mehdi
Khoramdel
Maryam
Sedghi
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.
Lattice
minimal prime ideal
zero-divisor graph
total graph
2018
07
01
15
27
http://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
9
1
On lifting of biadjoints and lax algebras
Fernando
Lucatelli Nunes
Given a pseudomonad $mathcal{T} $ on a $2$-category $mathfrak{B} $, if a right biadjoint $mathfrak{A}tomathfrak{B} $ has a lifting to the pseudoalgebras $mathfrak{A}tomathsf{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 <em>biadjoint triangle theorem</em> 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} tomathsf{Lax}textrm{-}mathcal{T}textrm{-}mathsf{Alg} _ell $ the inclusion, if $R: mathfrak{A}tomathfrak{B} $ is right biadjoint and has a lifting $J: mathfrak{A}to mathsf{Lax}textrm{-}mathcal{T}textrm{-}mathsf{Alg} $, then $ellcirc J$ is right biadjoint as well provided that $mathfrak{A} $ has some needed weighted bicolimits. In order to prove such result, we study <em>descent objects</em> and <em>lax descent objects</em>. At the last section, we study direct consequences of our theorems in the context of the $2$-monadic approach to coherence.
Lax algebras
pseudomonads
biadjunctions
adjoint triangles
lax descent objects
descent categories
weighted bi(co)limits
2018
07
01
29
58
http://cgasa.sbu.ac.ir/article_50747_e7751692a69d525e49259ebe2763142f.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
9
1
Pointfree topology version of image of real-valued continuous functions
Abolghasem
Karimi Feizabadi
Ali Akbar
Estaji
Maryam
Robat Sarpoushi
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 $C_c(X).$<br />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 <em>overlap</em>. 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 $f:Xrightarrowmathbb R$ and $ S subseteq mathbb R$.
frame
ring of real-valued continuous functions
countable image
$f$-ring
2018
07
01
59
75
http://cgasa.sbu.ac.ir/article_50745_d90d55e08316779860740922b0388294.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
9
1
Convergence and quantale-enriched categories
Dirk
Hofmann
Carla
D. Reis
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.
Ordered compact Hausdorff space
metric space
approach space
sober space
Cauchy completness
quantale-enriched category
2018
07
01
77
138
http://cgasa.sbu.ac.ir/article_58262_bab8553989f148c1daf7939ffd5b9f4d.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
9
1
Convex $L$-lattice subgroups in $L$-ordered groups
Rajabali
Borzooei
Fateme
Hosseini
Omid
Zahiri
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.
$L$-ordered group
convex $L$-subgroup
(normal) convex $L$-lattice subgroup
2018
07
01
139
161
http://cgasa.sbu.ac.ir/article_50748_0ee3783313053dea8791d1990de4c8e2.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
9
1
Persian Abstracts, Vol. 9, No. 1.
2018
07
01
172
182
http://cgasa.sbu.ac.ir/article_65931_d0ea46be4127864d66630e8a8548674d.pdf