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.