## Semicoverings: a generalization of covering space theory.(English)Zbl 1244.57010

The paper introduces semicoverings as a new generalization of classical coverings. A semicovering map is a local homeomorphism which admits continuous lifts of paths and homotopies. Additionally, lifts are required to continuously depend on the original map with respect to the compact-open topology.
The author develops basic properties of semicoverings and describes standard constructions as motivated by the classical theory of coverings. Many definitions, constructions and results are expressed in the language of category theory. The main result is the classification of semicoverings by induced covering morphisms (as functors on groupoids) for locally wep-spaces.
Reviewer: Ziga Virk (Litija)

### MSC:

 57M10 Covering spaces and low-dimensional topology 55Q52 Homotopy groups of special spaces
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