Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 22 Jul 2019 03:37:02 GMT2019-07-22T03:37:02Z50211Schreier split epimorphisms between monoidshttp://hdl.handle.net/10316/44056Title: Schreier split epimorphisms between monoids
Authors: Bourn, Dominique; Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela
Abstract: We explore some properties of Schreier split epimorphisms between monoids, which correspond to monoid actions. In particular, we prove that the split short five lemma holds for monoids, when it is restricted to Schreier split epimorphisms, and that any Schreier reflexive relation is transitive, partially recovering in monoids a classical property of Mal’tsev varieties.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/440562014-01-01T00:00:00ZSemidirect Products and Split Short Five Lemma in Normal Categorieshttp://hdl.handle.net/10316/44054Title: Semidirect Products and Split Short Five Lemma in Normal Categories
Authors: Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela
Abstract: In this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/440542014-01-01T00:00:00ZOn some categorical-algebraic conditions in S-protomodular categorieshttp://hdl.handle.net/10316/43919Title: On some categorical-algebraic conditions in S-protomodular categories
Authors: Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela
Abstract: In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular category, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Joónsson-Tarski varieties, raises a similar question: how to get a description of S-protomodular categories with a strong monoid-like behavior. In this paper we consider relative versions of the conditions mentioned above, in order to exhibit the parallelism with the "absolute" protomodular context and to obtain a hierarchy among S-protomodular categories.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/439192017-01-01T00:00:00ZSemidirect products and crossed modules in monoids with operationshttp://hdl.handle.net/10316/44047Title: Semidirect products and crossed modules in monoids with operations
Authors: Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela
Abstract: We describe actions, semidirect products and crossed modules in categories of monoids with operations. Moreover we characterize, in this context, the internal categories corresponding to crossed modules. Concrete examples in the cases of monoids, semirings and distributive lattices are given.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/440472013-01-01T00:00:00ZWhat 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/10316/440572014-01-01T00:00:00ZBaer sums of special Schreier extensions of monoidshttp://hdl.handle.net/10316/44059Title: Baer sums of special Schreier extensions of monoids
Authors: Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela
Abstract: We show that the special Schreier extensions of monoids, with abelian kernel, admit a Baer sum construction, which generalizes the classical one for group extensions with abelian kernel. In order to do that, we characterize the special Schreier extensions by means of factor sets.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/440592016-01-01T00:00:00ZFinite 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/10316/114682000-01-01T00:00:00ZFinite 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/10316/115571999-01-01T00:00:00ZKetotifen controlled release from cellulose acetate propionate and cellulose acetate butyrate membraneshttp://hdl.handle.net/10316/7804Title: Ketotifen controlled release from cellulose acetate propionate and cellulose acetate butyrate membranes
Authors: Sobral, Manuela; Sobral, Abilio; Guthrie, J.; Gil, M.
Abstract: Abstract Ketotifen was immobilised in cellulose acetate propionate (CAP) membranes and in cellulose acetate butyrate (CAB) membranes. The characteristics of each system were evaluated under a range of experimental conditions. The topography and uniformity of the membranes was assessed using scanning electron microscopy. The release characteristics associated with Ketotifen were monitored spectrophotometrically. The swelling capacity of the membranes was evaluated and attributed to the combined effects of diffusion and of complex dissociation, during swelling. The materials produced were able to provide controlled release of Ketotifen due to their controlled swelling behaviour and adequate release properties. The results showed that the release of Ketotifen from the CAB membranes is higher but the release from the CAP membranes is more uniform.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/78042008-01-01T00:00:00ZAnother Approach to Topological Descent Theoryhttp://hdl.handle.net/10316/7746Title: Another Approach to Topological Descent Theory
Authors: Sobral, Manuela
Abstract: In the category Top of topological spaces and continuous functions, we prove that surjective maps which are descent morphisms with respect to the class E of continuous bijections are exactly the descent morphisms, providing a new characterization of the latter in terms of subfibrations E(X) of the basic fibration given by Top/X which are, essentially, complete lattices. Also effective descent morphisms are characterized in terms of effective morphisms with respect to continuous bijections. For classes E satisfying suitable conditions, we show that the class of effective descent morphisms coincides with the one of effective E-descent morphisms.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10316/77462001-01-01T00:00:00ZLogic of implicationshttp://hdl.handle.net/10316/11380Title: Logic of implications
Authors: Adámek, Jirí; Sobral, Manuela; Sousa, Lurdes
Abstract: A sound and complete logic for implications (or quasi-equations) is
presented, extending naturally Birkhoff’s equational logic. This is based on a general
logic for injectivity, following an idea of G. Ro¸su.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/113802005-01-01T00:00:00ZDescent for Priestley Spaceshttp://hdl.handle.net/10316/11393Title: Descent for Priestley Spaces
Authors: Dias, Margarida; Sobral, Manuela
Abstract: A characterization of descent morphism in the category of Priestley
spaces, as well as necessary and su cient conditions for such morphisms to be e ective
are given. For that we embed this category in suitable categories of preordered
topological spaces were descent and e ective morphisms are described using the
monadic description of descent.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/113932005-01-01T00:00:00ZDescent 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/10316/111942009-01-01T00:00:00ZDescent for discrete (co)fibrationshttp://hdl.handle.net/10316/11440Title: Descent for discrete (co)fibrations
Authors: Sobral, Manuela
Abstract: We characterize the (e ective) E-descent morphisms in the category
Cat of small categories, when E is the class of discrete fibrations or the one of
discrete co fibrations, and prove that every e ective global-descent morphism is an
e ective E-descent morphism while its converse fails.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114402003-01-01T00:00:00ZOn functors which are lax epimorphismshttp://hdl.handle.net/10316/11460Title: On functors which are lax epimorphisms
Authors: Adámek, Jirí; Bashir, Robert El; Sobral, Manuela; Velebil, Jirí
Abstract: We show that lax epimorphisms in the category Cat are precisely the functors P : Ε → B for which the functor P* : [B, Set] → [E, Set] of composition with P is fully faithful. We present two other characterizations. Firstly, lax epimorphisms are precisely the ``absolutely dense'' functors, i.e., functors P such that every object B of B is an absolute colimit of all arrows P(E) → B for E in E. Secondly, lax epimorphisms are precisely the functors P such that for every morphism f of B the category of all factorizations through objects of P[E] is connected.
A relationship between pseudoepimorphisms and lax epimorphisms is discussed.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10316/114602001-01-01T00:00:00ZOn categories with semidirect productshttp://hdl.handle.net/10316/14325Title: On categories with semidirect products
Authors: Martins-Ferreira, Nelson; Sobral, Manuela
Abstract: We characterize pointed categories having semidirect products in the
sense of D. Bourn and G. Janelidze ([3]) providing necessary and sufficient conditions
for a pointed category to admit semidirect products and interpreting these
conditions in terms of protomodularity and exactness of certain split chains.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/143252010-01-01T00:00:00ZAnother approach to topological descent theoryhttp://hdl.handle.net/10316/11229Title: Another approach to topological descent theory
Authors: Sobral, Manuela
Abstract: In the category Top of topological spaces and continuous functions, we prove that descent
morphisms with respect to the class IE of continuous bijections are exactly the descent morphisms, providing a new characterization of the latter in terms of subfibrations IE(X) of the
basic fibration given by Top/X which are, essentially, complete lattices. Also effective descent
morphisms are characterized in terms of effective morphisms with respect to continuous bijections. For classes IE satisfying suitable conditions, we show that the class of effective descent
morphisms coincides with the one of effective IE-descent morphisms.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10316/112291998-01-01T00:00:00ZProfinite 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/10316/112392008-01-01T00:00:00ZA logic of implications in algebra and coalgebrahttp://hdl.handle.net/10316/11299Title: A logic of implications in algebra and coalgebra
Authors: Adámek, Jirí; Sobral, Manuela; Sousa, Lurdes
Abstract: Implications in a category can be presented as epimorphisms: an ob-
ject satis¯es the implication i® it is injective w.r.t. that epimorphism. G. Ro»cu
formulated a logic for deriving an implication from other implications. We present
two versions of implicational logics: a general one and a ¯nitary one (for epimor-
phisms with ¯nitely presentable domains and codomains). In categories Alg § of
algebras on a given signature our logic specializes to the implicational logic of R.
Quackenbush. In categories Coalg H of coalgebras for a given accessible endofunctor
H of sets we derive a logic for implications in the sense of P. Gumm.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/112992007-01-01T00:00:00ZDescent 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/10316/112372008-01-01T00:00:00ZMorita equivalence of many-sorted algebraic theorieshttp://hdl.handle.net/10316/4616Title: Morita equivalence of many-sorted algebraic theories
Authors: Adámek, Jirí; Sobral, Manuela; Sousa, Lurdes
Abstract: Algebraic theories are called Morita equivalent provided that the corresponding varieties of algebras are equivalent. Generalizing Dukarm's result from one-sorted theories to many-sorted ones, we prove that all theories Morita equivalent to an S-sorted theory are obtained as idempotent modifications of . This is analogous to the classical result of Morita that all rings Morita equivalent to a ring R are obtained as idempotent modifications of matrix rings of R.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/46162006-01-01T00:00:00Z