Consider three functions \$$L, C, R \$$ where \$$C : A \rightarrow B \$$ and \$$L, R : B \rightarrow A \$$.
Where \$$L \$$ and \$$R \$$ are left and right adjoint to \$$C \$$ respectively.
This implies that \$$C \$$ is left adjoint to \$$R \$$ and right adjoint to \$$L \$$.
\$$R \$$ is the approximate inverse of \$$C \$$ from above and \$$L \$$ is the approximate inverse of \$$C \$$ from below. I am tempted to call them limits.
The error is in treating \$$L \$$ and \$$R \$$ as if they were left and right ajoints of each other, **they are not**.
What is the relationship between \$$L \$$ and \$$R \$$?
It appears that they act as bounds for the true value in \$$C \$$.