THE HUREWICZ THEOREM IN Sh*? AND Sh*2 ?

. The Hurewicz isomorphism theorem relating coarse shape groups and coarse shape homology groups of pointed metric continua is proved. A similar statement is proposed and proved in the category Sh*2 for relative coarse shape pro-groups and coarse shape homology pro-groups, and consequently a relative variant for relative coarse shape groups and coarse shape homology groups of pointed pairs of metric continua is given.