Singular chain

Definition
A singular $$n$$-chain is defined as a formal linear combination of singular $$n$$-simplices (see defining ingredient::singular simplex), with integer coefficients. The set of all singular $$n$$-chains forms an Abelian group under coordinate-wise addition. This is in fact the free abelian group on the singular $$n$$-simplices, and is termed the $$n^{th}$$ chain group.