## Reference Request – Limitation of a co-calibration to closed subspaces

To let $$i: X rightarrow Y$$ be a co-calibration between CW complexes. To let $$A$$ be a closed subspace of $$Y$$ and $$Z = i ^ {- 1} (A)$$, To let $$j: Z rightarrow A$$ be the limitation of $$i$$ to $$Z$$, Which of the following statements is true?

1. $$j$$ is a co-calibration.
2. The cofaser sequence $$Z rightarrow A rightarrow Z / A$$ induces a long exact sequence in homology.

If the above statements are generally wrong. I was wondering if they have come true if we accept that $$i: X rightarrow Y$$ be a cellular embedding between CW complexes.