Uniformly Movable Categories And Uniform Movability Of Topological Spaces

TL;DR

This paper generalizes the concept of movability in topology using category theory, establishing a link between uniformly movable categories and uniformly movable topological spaces through homotopy categories.

Contribution

It introduces the notion of uniformly movable categories and proves their equivalence to uniformly movable topological spaces within the framework of shape theory.

Findings

A topological space is uniformly movable iff its comma category in HTop over HPol is uniformly movable.

The paper extends the categorical concept of movability to a weaker, uniform version.

Establishes a categorical characterization of uniform movability in shape theory.

Abstract

A categorical generalization of the notion of movability from the inverse systems and shape theory was given by the first author who defined the notion of movable category and interpreted by this the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of the shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is a uniformly movable category. This is a weakened version of the categorical notion of uniform movability introduced by the second author.