Let $\mathcal{C}$ be the category of bounded cochain complexes of $R$-modules for a commutative ring $R$. I am trying to prove the following formula involving determinant $\text{Det}(F)$ of a map of chain complexes $F^* : C^* \rightarrow C^*$:

$$\text{Det}(F) = \prod_{i = 0}^n (-1)^n \text{det}(F^i : C^i \rightarrow C^i)$$

I am hoping there is a notion of determinant of chain complexes such that this formula will hold, but I also want to construct it a more canonical way. There should be a wedge product $\Lambda^i C^*$. My question is whether someone can make sense of determinant of chain complexes in a way where this property holds.