Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 09 Dec 2022 05:00:42 GMT2022-12-09T05:00:42Z50141Split extensions and semidirect products of unitary magmashttp://hdl.handle.net/10316/89459Title: Split extensions and semidirect products of unitary magmas
Authors: Gran, Marino; Janelidze, George; Sobral, Manuela
Abstract: We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10316/894592019-01-01T00:00:00ZOn exponentiability of étale algebraic homomorphismshttp://hdl.handle.net/10316/43640Title: On exponentiability of étale algebraic homomorphisms
Authors: Clementino, Maria Manuel; Hofmann, Dirk; Janelidze, George
Abstract: In this paper we show that the theorem, by Cagliari and Mantovani, stating that in
the category of compact Hausdorff spaces every étale map is exponentiable, can be formulated
in a general category Alg(T) of Eilenberg-Moore T-algebras, for a monad T, and proved in
case T satisfies the so-called Beck-Chevalley condition. For that, Alg(T) is embedded in the
(topological) category RelAlg(T) of relational T-algebras, where a suitable notion of étale
morphism can be studied, it is shown that morphisms between T-algebras are exponentiable in
RelAlg(T), and, moreover, these exponentials belong to Alg(T) whenever the morphisms are
étale.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/436402013-01-01T00:00:00ZThe monads of classical algebra are seldom weakly cartesianhttp://hdl.handle.net/10316/44482Title: The monads of classical algebra are seldom weakly cartesian
Authors: Clementino, Maria Manuel; Hofmann, Dirk; Janelidze, George
Abstract: This paper begins a systematic study of weakly cartesian properties of monads that determine familiar varieties of universal algebras. While these properties clearly fail to hold for groups, rings, and many other related classical algebraic structures, their analysis becomes non-trivial in the case of semimodules over semirings, to which our main results are devoted. In particular necessary and sufficient conditions on a semiring S, under which the free semimodule monad has: (a) its underlying functor weakly cartesian, (b) its unit a weakly cartesian natural transformation, (c) its multiplication a weakly cartesian natural transformation, are obtained.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/444822013-01-01T00:00:00ZOn Exponentiable Morphisms in Classical Algebrahttp://hdl.handle.net/10316/41050Title: On Exponentiable Morphisms in Classical Algebra
Authors: Clementino, Maria Manuel; Hofmann, Dirk; Janelidze, George
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/410502016-01-01T00:00:00ZWhat are effective descent morphisms of Priestley spaces?http://hdl.handle.net/10316/44057Title: What are effective descent morphisms of Priestley spaces?
Authors: Janelidze, George; Sobral, Manuela
Abstract: We discuss the problem formulated in the title. We solve it only in two very special cases: for maps with finite codomains and for maps that are open and order-open, or, equivalently, open and order-closed.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/440572014-01-01T00:00:00ZAnother note on effective descent morphisms of topological spaces and relational algebrashttp://hdl.handle.net/10316/89423Title: Another note on effective descent morphisms of topological spaces and relational algebras
Authors: Clementino, Maria Manuel; Janelidze, George
Abstract: We make three independent observations on characterizing effective descent morphisms in the category of topological spaces. The first of them proposes a new modification of known characterizations of effective descent morphisms of general spaces, while the other two are devoted to locally finite and Hausdorff spaces, respectively. The Hausdorff case is considered, as far as we could, at the more general level of relational algebras in the sense of M. Barr.
Sun, 01 Mar 2020 00:00:00 GMThttp://hdl.handle.net/10316/894232020-03-01T00:00:00ZStrict monadic topology I: First separation axioms and reflectionshttp://hdl.handle.net/10316/89438Title: Strict monadic topology I: First separation axioms and reflections
Authors: Janelidze, George; Sobral, Manuela
Abstract: Given a monad T on the category of sets, we consider reflections of Alg(T) into its full subcategories formed by algebras satisfying natural counterparts of topological separation axioms T_0, T_1, T_2, T_ts, and T_ths; here ts stands for totally separated and ths for what we call totally homomorphically separated, which coincides with ts in the (compact Hausdorff) topological case. We ask whether these reflections satisfy simple conditions useful in categorical Galois theory, and give some partial answers in easy cases.
Sun, 01 Mar 2020 00:00:00 GMThttp://hdl.handle.net/10316/894382020-03-01T00:00:00ZSome remarks on protolocalizations and protoadditive reﬂectionshttp://hdl.handle.net/10316/89422Title: Some remarks on protolocalizations and protoadditive reﬂections
Authors: Clementino, Maria Manuel; Gran, Marino; Janelidze, George
Abstract: We investigate additional properties of protolocalizations, introduced and studied by Borceux, Clementino, Gran, and Sousa, and of protoadditive reﬂections, introduced and studied by Everaert and Gran. Among other things, we show that there are no nontrivial (protolocalizations and) protoadditive reﬂections of the category of groups, and establish a connection between protolocalizations and Kurosh–Amitsur radicals of groups with multiple operators whose semisimple classes form subvarieties.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10316/894222018-01-01T00:00:00ZLocal homeomorphisms via ultrafilter convergencehttp://hdl.handle.net/10316/11436Title: Local homeomorphisms via ultrafilter convergence
Authors: Clementino, Maria Manuel; Hofmann, Dirk; Janelidze, George
Abstract: Using the ultrafilter-convergence description of topological spaces,
we generalize Janelidze-Sobral characterization of local homeomorphisms
between finite topological spaces, showing that local homeomorphisms are
the pullback-stable discrete fibrations.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114362003-01-01T00:00:00ZFinite preorders and topological descenthttp://hdl.handle.net/10316/11557Title: Finite preorders and topological descent
Authors: Janelidze, George; Sobral, Manuela
Abstract: It is shown that the descent constructions of finite preorders provide a simple motivation for
those of topological spaces, and new counter-examples to open problems in Topological descent
theory are constructed
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/115571999-01-01T00:00:00ZFinite preorders and topological descent II: étale descenthttp://hdl.handle.net/10316/11468Title: Finite preorders and topological descent II: étale descent
Authors: Janelidze, George; Sobral, Manuela
Abstract: It is known that every effective (global-) descent morphism of topological spaces is an effective etale-descent morphism. On the other hand, in the predecessor of this paper we gave examples of: a descent morphism that is not an effective etale-descent morphism; an effective etale-descent morphism that is not a descent morphism. Both of the examples in fact involved only finite topological spaces, i.e. just finite preorders, and now we characterize the effective etale-descent morphisms of preorders/finite topological spaces completely.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10316/114682000-01-01T00:00:00ZProfinite relational structureshttp://hdl.handle.net/10316/11239Title: Profinite relational structures
Authors: Janelidze, George; Sobral, Manuela
Abstract: We show that a topological preorder (on a Stone space) is profinite if
and only if it is inter-clopen, i.e. it can be presented as an intersection of closed-andopen
preorders on the same space. In particular this provides a new characterization
of the so-called Priestley spaces. We then extend this from preorders to general relational
structures satisfying some conditions. We also give a stronger condition
that has a rather clear model-theoretic meaning.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112392008-01-01T00:00:00ZDescent for compact 0-dimensional spaceshttp://hdl.handle.net/10316/11237Title: Descent for compact 0-dimensional spaces
Authors: Janelidze, George; Sobral, Manuela
Abstract: Using the reflection of the category C of compact 0-dimensional topological
spaces into the category of Stone spaces we introduce a concept of a fibration
in C. We show that: (i) effective descent morphisms in C are the same as the surjective
fibrations; (ii) effective descent morphisms in C with respect to the fibrations
are all surjections.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112372008-01-01T00:00:00ZDescent for regular epimorphisms in Barr exact Goursat categorieshttp://hdl.handle.net/10316/11194Title: Descent for regular epimorphisms in Barr exact Goursat categories
Authors: Janelidze, George; Sobral, Manuela
Abstract: We show that the category of regular epimorphisms in a Barr exact
Goursat category is almost Barr exact in the sense that (it is a regular category
and) every regular epimorphism in it is an e ective descent morphism.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/111942009-01-01T00:00:00Z