NOTES ON HOMOTOPY PULL-BACKS

Abstract

In these notes we investigate the relationships between two different notions of homotopy pull-back, namely Mather's original concept for homotopy commutative squares (1976) and Baues' notion for commutative squares in his book on algebraic homotopy (1989) (which does not contain any reference to Mather's work. In fact, Baues' definition seems to be based on investigations by V. Puppe (1974)). We also provide new characterizations of the two concepts; in particular we introduce a homotopy pull-back property for Baues' homotopy pull-backs.