$i_1\dashv i^1\dashv i_2\dashv i^2\dashv\dots$ ...if $i_j$ are full and faithful. $i_1\stackrel{\eta_12 i_1}{\to} i_2 i^1 i_1\stackrel{\sim}{\to} i_2\stackrel{\eta_23 i_2}{\to}i_3 i^2 i_2\stackrel{\sim}{\to}i_3$