Is homology an adjoint functor?

Consider the homology functor $H$ defined (say) on the category of complexes of R-modules (where $R$ is unitary commutative ring). Does $H$ admits left or right adjoints? I know that homology preserves direct sums and direct limits, so it seems reasonable to think of it as a left adjoint.

I also believe that homology cannot be a right adjoint, since in general it does not preserve inverse limits. Is this correct?

Sorry if the question is naive, I'm studying homological algbera directly from a course in algebraic topology.

As comments have pointed out, homology does not preserve cokernels for example. The functors that are adjoints, however, and this is a bit more important for example when you're doing model theory and homotopy theory with objects with a differential, are the boundary and cycles functor.

Namely, the functor from the category of complexes $\textsf {Ch}$ that assigns $C$ to $Z_n(C)$ is in fact of the form $\hom_{\textsf {Ch}}(S^n,C)$ where $S^n$ is the complex generated by a single element $z$ in degree $n$ with $dz=0$. Similarly, the functor $C\longmapsto B_n(C)$ is of the form $\hom_{\textsf {Ch}}(D^{n+1},C)$ where $D^{n+1}$ is the complex with two generators $x$ and $y$ in degrees $n+1$ and $n$ and with $dx=y$. The natural inclusion $S^n\subseteq D^{n+1}$ then induces the inclusion map $B_n(Z) \subseteq Z_n(C)$, and homology is, at least, a `quotient of representable functors.'