H-group

An H-space whose multiplication is homotopy associative and admits a homotopy inverse. These operations give $[X,Y{]}_{\ast }$ a group structure for every based CW complex $X$. A loop space is the basic example: concatenate paths, use reversal for inversion, and use reparametrization for homotopy associativity. A bare H-space should not automatically be treated as a group object.