Lambek invariants in a p-semi-abelian category

We consider the well-known invariants $\mathrm{Ker}$ and $\mathrm{Img}$ for commutative squares in P-semi-abelian categories. These invariants were introduced by Lambek for groups and then studied in a more general context by Hilton and Nomura. In this paper, P-semi-abelian analogs are proved for Lambek's isomorphism and acyclic sequences that include these invariants are found.