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On covariant topological functors. I. (English) Zbl 0707.54010
Following E. V. Shchepin, a functor from the category HComp of compact Hausdorff spaces into itself is called normal provided it preserves monomorphisms, epimorphisms, projective limits, intersections, pullbacks along monomorphisms, initial and final objects and weight. The author surveys results on normal functors, exhibiting in particular several characterizations of the Vietoris hyperspace functor among normal functors, investigates the quasicategory of normal functors, analyses normal monads on HComp, and extends the whole theory by investigating various concepts weaker than normality.
Reviewer: H.Herrlich

54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
54B20 Hyperspaces in general topology
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads