$$ for any such diagram, and define $$\bK_0(\m V/X \xrightarrow{f}  Y) := \frac{\bM(\m V/X \xrightarrow{f}  Y)} {\mathbb {BL}(\m V/X \xrightarrow{f}  Y)}.$$ The corresponding equivalence class of $[V \xrightarrow{p}  X]$ shall be denoted by $\Bigl[[V \xrightarrow{p}  X] \Bigr].$  Note that 