Manuela Sobral

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We show that lax epimorphisms in the category Cat are precisely the functors P : E −→ 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(More)
The paper deals with (effective) descent morphisms for subfibrations E(X) of the basic fibration Top~X, for topological spaces X and classes E of continuous functions stable under pullback. For a category with pullbacks, we prove the stability under pullback of effective Edescent morphisms for a class E satisfying some suitable conditions. This plays a r61e(More)
Implications in a category can be presented as epimorphisms: an object satisfies the implication iff it is injective w.r.t. that epimorphism. G. Roçu formulated a logic for deriving an implication from other implications. We present two versions of implicational logics: a general one and a finitary one (for epimorphisms with finitely presentable domains and(More)
A characterization of descent morphism in the category of Priestley spaces, as well as necessary and sufficient conditions for such morphisms to be effective are given. For that we embed this category in suitable categories of preordered topological spaces were descent and effective morphisms are described using the monadic description of descent.
We characterize the (effective) E-descent morphisms in the category Cat of small categories, when E is the class of discrete fibrations or the one of discrete cofibrations, and prove that every effective global-descent morphism is an effective E-descent morphism while its converse fails.
The categorical definition of semidirect products was introduced by D. Bourn and G. Janelidze in [2], where they proved that, in the category of groups, this notion coincides with the classical one. A characterization of pointed categories with categorical semidirect products was given in [3]. The existence of such products imply, in particular, that the(More)
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 mor phisms providing a new characterization of the latter in terms of sub brations IE X of the basic bration given by Top X which are essentially complete lattices Also e ective(More)
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