Abstract:

This paper defines homotopy regular morphisms in the category of topological spaces with base point and discusses its existence conditions, properties and the close relationships to homotopy monomorphism (epimorphism), homotopy regular monorphism (epimorphism) and homototy equivalence.

Key words: Ｈｏｍｏｔｏｐｙｍｏｎｏｍｏｒｐｈｉｓｍ （ｅｐｉｍｏｒｐｈｉｓｍ）, Ｈｏｍｏｔｏｐｙｒｅｇｕｌａｒｍｏｎｏｍｏｒｐｈｉｓｍ（ｅｐｉｍｏｒｐｈｉｓｍ）, Ｈｏｍｏｔｏｐｙｅｑｕｉｖａｌｅｎｃｅ, Ｈｏｍｏｔｏｐｙｒｅｇｕｌａｒｍｏｒｐｈｉｓｍ, Ｓｔａｎｄａｒｄｄｅｃｏｍｐｏｓｉｔｉｏｎ．