An algebraic description of regular epimorphisms in topology. (English) Zbl 1072.18002
A regular epimorphism in an arbitrary category is a morphism which is a coequalizer of some pair of parallel morphisms. They are usually seen as “good” epimorphisms but their concrete description is often a problem. This paper provides a description of regular epimorphisms in the category of topological spaces and in some other similar categories, in terms of convergence of ultrafiters. This result is a special instance of a more general one on regular epimorphisms of \((T; \,V)\)-algebras where \(V\) is a symmetric monoidal closed complete lattice and \(T\) is a \(V\)-admissible monad on \({\mathcal S}et\).
Reviewer: Y. Diers (Faches-Thumesnil)
MSC:
18A20 | Epimorphisms, monomorphisms, special classes of morphisms, null morphisms |
18B30 | Categories of topological spaces and continuous mappings (MSC2010) |
18B35 | Preorders, orders, domains and lattices (viewed as categories) |
18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
18C20 | Eilenberg-Moore and Kleisli constructions for monads |
54B30 | Categorical methods in general topology |
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