For each monic $ fcolon ato d $ there is one and only one $ mathcal{C} $ - arrow $ chi_{f}:dtoOmega $ such that $ begin{CD}a@>{f}>{}>d!Bigg{downarrow}@V{}V{}V_{chi_{f}}V 1@>{mathit{true}}>{}>Omegaend{CD} $ is a pullback square. The arrow $ chi_{f} $ is called the characteristic arrow