关于覆叠同伦正则态射

On covering homotopy regular morphisms

目的在点标道路连通CW空间的同伦范畴中，引进覆叠同伦正则态射的概念，研究它存在的条件、性质以及它与覆叠同伦单（满）态和覆叠同伦等价之间的关系。方法利用万有覆叠函子，将映射f：X→Y的研究转化为对它在万有覆叠空间上诱导的映射f：X（0）→Y（0）进行研究。结果推广了同胚映射、同伦等价和同伦正则态射的有关结果。结论若f为同伦正则态射,则f必为覆叠同伦正则态射；若f为覆叠同伦正则态射，则f不一定是同伦正则态射。

Aim To define covering homotopy regular morphism in the homotopy category of pointed path-connected CW-spaces. To discuss its existence conditions, properties and the close relationships to covering homotopy monomorphism （epimorphism） and covering homotopy equivalence. Methods The studies on the map f： X → Y are transfered to the studies on the map f：X（0） → Y（0） that is induced by universal covering spaces by using universal covering functor. Results Generalizing some results of homeomorphic morphism, homotopy equivalence and homotopy regular morphism. Conclusion The map f is a covering homotopy regular morphism if it is a homotopy regular morphism; The map f is not surely a homotopy regular morphism if it is a covering homotopy regular morphism.