Some criterion of movability
by
P. S. Gevorgyan
Moscow State University

The notion of movability for metrizable compacts was introduced by K. Borsuk. We define the notion of movable category and prove that the movability of a topological space X coincides with the movability of a suitable category, which is generated by the topological space X (i.e. the category W^X, defined by S. Mardesic).

Let K be an arbitrary category and K' any subcategory of category K.

DEFINITION 1. We say that subcategory K' is movable in category K, if for any object X in ob(K') there exists an object Y in ob(K') and a morphism f  in   K'(X, Y) such that for any object Z in ob(K') and any morphism g in K'(Z, X) there is a morphism h in K(Y, Z) which satisfies the condition g o h = f.

DEFINITION 2. We say that a category is movable if it is movable in itself.

THEOREM 1. Any category K with zero-morphisms is movable.

THEOREM 2. Any category K with initial objects is movable.

THEOREM 3. The topological space X is movable if and only if the category W^X defined by S. Mardesic is movable.

Paper reference: arXiv:math.GN/0105058

Date received: June 22, 2001