Effective Descent Morphisms in Categories of Lax Algebras

Effective Descent Morphisms in Categories of Lax Algebras

In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...

Covering Morphisms in Categories of Relational Algebras

In this paper we use Janelidze’s approach to the classical theory of topological coverings via categorical Galois theory to study coverings in categories of relational algebras. Moreover, we present characterizations of effective descent morphisms in the categories of M ordered sets and of multi-ordered sets.

Exponentiability in categories of lax algebras

For a complete cartesian-closed category V with coproducts, and for any pointed endofunctor T of the category of sets satisfying a suitable Beck-Chevalley-type condition, it is shown that the category of lax reflexive (T,V)-algebras is a quasitopos. This result encompasses many known and new examples of quasitopoi. Mathematics Subject Classification: 18C20, 18D15, 18A05, 18B30, 18B35.

Partial Morphisms in Categories of Effective Objects

Universality of Coproducts in Categories of Lax Algebras

Categories of lax (T, V )-algebras are shown to have pullbackstable coproducts if T preserves inverse images. The general result not only gives a common proof of this property in many topological categories but also shows that important topological categories, like the category of uniform spaces, are not presentable as a category of lax (T, V )-algebras, with T preserving inverse images. Moreov...