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On lifting of biadjoints and lax algebras 关于双关节和松弛代数的提升
Categories and General Algebraic Structures with Application Pub Date : 2018-07-01 DOI: 10.29252/cgasa.9.1.29
Fernando Lucatelli Nunes
{"title":"On lifting of biadjoints and lax algebras","authors":"Fernando Lucatelli Nunes","doi":"10.29252/cgasa.9.1.29","DOIUrl":"https://doi.org/10.29252/cgasa.9.1.29","url":null,"abstract":"","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123102559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Pointfree topology version of image of real-valued continuous functions 实值连续函数图像的无点拓扑版本
Categories and General Algebraic Structures with Application Pub Date : 2018-07-01 DOI: 10.29252/CGASA.9.1.59
A. K. Feizabadi, A. Estaji, M. R. Sarpoushi
{"title":"Pointfree topology version of image of real-valued continuous functions","authors":"A. K. Feizabadi, A. Estaji, M. R. Sarpoushi","doi":"10.29252/CGASA.9.1.59","DOIUrl":"https://doi.org/10.29252/CGASA.9.1.59","url":null,"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 $f:Xrightarrowmathbb R$ and $ S subseteq mathbb R$.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115070097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Total graph of a $0$-distributive lattice $0$-分配格的总图
Categories and General Algebraic Structures with Application Pub Date : 2018-07-01 DOI: 10.29252/CGASA.9.1.15
S. E. Atani, Saboura Dolati Pishhesari, M. Khoramdel, M. Sedghi
{"title":"Total graph of a $0$-distributive lattice","authors":"S. E. Atani, Saboura Dolati Pishhesari, M. Khoramdel, M. Sedghi","doi":"10.29252/CGASA.9.1.15","DOIUrl":"https://doi.org/10.29252/CGASA.9.1.15","url":null,"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.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127638319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Convex $L$-lattice subgroups in $L$-ordered groups L序群中的凸L格子群
Categories and General Algebraic Structures with Application Pub Date : 2018-07-01 DOI: 10.29252/CGASA.9.1.139
R. Borzooei, F. Hosseini, O. Zahiri
{"title":"Convex $L$-lattice subgroups in $L$-ordered groups","authors":"R. Borzooei, F. Hosseini, O. Zahiri","doi":"10.29252/CGASA.9.1.139","DOIUrl":"https://doi.org/10.29252/CGASA.9.1.139","url":null,"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.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130762252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit 弱单位阿基米德$ell$-群中$H$-闭单反射的表示
Categories and General Algebraic Structures with Application Pub Date : 2018-07-01 DOI: 10.29252/CGASA.9.1.1
B. Banaschewski, A. Hager
{"title":"Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit","authors":"B. Banaschewski, A. Hager","doi":"10.29252/CGASA.9.1.1","DOIUrl":"https://doi.org/10.29252/CGASA.9.1.1","url":null,"abstract":"The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ 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 $C(T)$.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125319350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Convergence and quantale-enriched categories 收敛和富量子范畴
Categories and General Algebraic Structures with Application Pub Date : 2017-05-24 DOI: 10.29252/CGASA.9.1.77
Dirk Hofmann, C. Reis
{"title":"Convergence and quantale-enriched categories","authors":"Dirk Hofmann, C. Reis","doi":"10.29252/CGASA.9.1.77","DOIUrl":"https://doi.org/10.29252/CGASA.9.1.77","url":null,"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 $mathcal{V}$-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.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132412771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Witt rings of quadratically presentable fields 二次可呈现域的维特环
Categories and General Algebraic Structures with Application Pub Date : 2017-05-12 DOI: 10.29252/CGASA.12.1.1
Paweł Gładki, K. Worytkiewicz
{"title":"Witt rings of quadratically presentable fields","authors":"Paweł Gładki, K. Worytkiewicz","doi":"10.29252/CGASA.12.1.1","DOIUrl":"https://doi.org/10.29252/CGASA.12.1.1","url":null,"abstract":"This paper introduces a novel approach to the axiomatic theory of quadratic forms. We work internally in a category of certain partially ordered sets, subject to additional conditions which amount to a strong form of local presentability. We call such partial orders presentable. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of quadratically presentable fields, that is fields equipped with a presentable partial order inequationaly compatible with the algebraic operations. As an application, we show that Witt rings of symmetric bilinear forms over fields, of both characteristic 2 and not 2, are isomorphic to Witt rings of suitably built quadratically presentable fields, which therefore provide a uniform construction of Witt rings for all characteristics.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129339342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Another proof of Banaschewski's surjection theorem Banaschewski抛射定理的另一个证明
Categories and General Algebraic Structures with Application Pub Date : 1900-01-01 DOI: 10.29252/CGASA.11.1.113
D. Baboolal, J. Picado, A. Pultr
{"title":"Another proof of Banaschewski's surjection theorem","authors":"D. Baboolal, J. Picado, A. Pultr","doi":"10.29252/CGASA.11.1.113","DOIUrl":"https://doi.org/10.29252/CGASA.11.1.113","url":null,"abstract":"We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities (\"not necessarily symmetric uniformities\"). Further, we show how a (regular) Cauchy point on a closed uniform sublocale can be extended to a (regular) Cauchy point on the larger (quasi-)uniform frame.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124059998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On GPW-Flat Acts 关于gww - flat法案
Categories and General Algebraic Structures with Application Pub Date : 1900-01-01 DOI: 10.29252/CGASA.12.1.25
H. Rashidi, A. Golchin, H. M. Saany
{"title":"On GPW-Flat Acts","authors":"H. Rashidi, A. Golchin, H. M. Saany","doi":"10.29252/CGASA.12.1.25","DOIUrl":"https://doi.org/10.29252/CGASA.12.1.25","url":null,"abstract":"In this article, we present GPW-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right S-act A_{S} is GPW-flat if for every s in S, there exists a natural number n = n_ {(s, A_{S})} in mathbb{N} such that the functor A_{S} otimes {}_{S}- preserves the embedding of the principal left ideal {}_{S}(Ss^n) into {}_{S}S. We show that a right S-act A_{S} is GPW-flat if and only if for every s in S there exists a natural number n = n_{(s, A_{S})} in mathbb{N} such that the corresponding varphi is surjective for the pullback diagram P(Ss^n, Ss^n, iota, iota, S), where iota : {}_{S}(Ss^n) rightarrow {}_{S}S is a monomorphism of left S-acts. Also we give some general properties and a characterization of monoids for which this condition of their acts implies some other properties and vice versa.","PeriodicalId":170235,"journal":{"name":"Categories and General Algebraic Structures with Application","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134281441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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