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On categories with semidirect products

Martins-Ferreira, Nelson; Sobral, Manuela

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.


Descent for regular epimorphisms in Barr exact Goursat categories

Janelidze, George; Sobral, Manuela

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. ; FCT/Centro de Matemática da Universidade de Coimbra; South African NRF


Descent for compact 0-dimensional spaces

Janelidze, George; Sobral, Manuela

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.


Profinite relational structures

Janelidze, George; Sobral, Manuela

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...


Ketotifen controlled release from cellulose acetate propionate and cellulose ac...

Sobral, Manuela; Sobral, Abilio; Guthrie, J.; Gil, M.

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...


A logic of implications in algebra and coalgebra

Adámek, Jirí; Sobral, Manuela; Sousa, Lurdes

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 give...


Morita equivalence of many-sorted algebraic theories

Adámek, Jirí; Sobral, Manuela; Sousa, Lurdes

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 obtaine...


Logic of implications

Adámek, Jirí; Sobral, Manuela; Sousa, Lurdes

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. ; Centre for Mathematics of University of Coimbra/ FCT; International Center for Mathematics; Ministry of Education of the Czech Republic, Project MSM 6840770014; School of Technology of Viseu


Descent for Priestley Spaces

Dias, Margarida; Sobral, Manuela

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. ; FCT/Centro de Matemática da Universidade de Coimbra


Descent for discrete (co)fibrations

Sobral, Manuela

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. ; The Fields Institute, ATLANTIS 98-00-CAN-0017-00; INTAS 97-31961


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