Let $\mathcal{C}$ be a closed symmetric monoidal Grothendieck category. Then there are two general notions of purity in $\mathcal{C}$, the $\lambda$-purity and the $\otimes$-purity. Let $f:A\to B$ be a morphism in $\mathcal{C}$. $f$ is called $\lambda$-pure if for any commutative diagram$\require{AMScd}$ \begin{CD} A' @>f'>> B' \\ @VuVV @VVvV \\ A @>>f> B \end{CD} there exists a map $g:B'\to A$ such that $u=g\circ f'$. One can see that every $\lambda$-pure morphism is a monomorphism. A monomorphism $f:X\to Y$ is said to be $\otimes$-pure if for any object $Z$ in $\mathcal{C}$, $f\otimes Z$ is monic. One can see that every $\lambda$-pure monomorphism is $\otimes$-pure. Now let us consider the category of chain complexes of $\mathcal{C}$ and denote it by $\mathbb{C}(\mathcal{C})$.

How can I define the notion of purity in $\mathbb{C}(\mathcal{C})$?