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.
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
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.
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...
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...
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...
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...
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
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
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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