A concept of homotopy regular monomorphism is introduced which is strictly between homotopy monomorphism and homotopy equivalence. And it characterizes homotopy equivalence in some sense.
Recall that f: X→Y is a homotopy epimorphism (monomorphism) if given u, v: Y→W(u, v:W→X), u(?)of(?)v(?)f implies u(?)v(f(?)u(?)f(?)v implies u(?)v). In ref. [1], Lin and Shen
Project supported by the National Natural Science Foundation of China.
Recall that f: X→Y is a homotopy epimorphism (monomorphism), if given u, v: Y→W (u, v: W→X), uofvof implies uv (foufov implies uv). In this note, we shall consider the localization of homotopy epimorphisms andmonom...