Differential group

An Abelian group $C$ with a given endomorphism $d : C \rightarrow C$ such that $d^2 = 0$. This endomorphism is called a differential. The elements of a differential group are known as chains; the elements of the kernel $\ker d$ are known as cycles; and the elements of the image $\mathrm{im}\, d$ are called boundaries. The homology of $C$ is the quotient $\ker d / \mathrm{im}\,d$.

References

[a1]	E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. 156