The homotopy category of chain complexes can also be interpreted along these lines.
The basic object is the category of chain complexes in .
The boundary operation on a simplex induces a singular chain complex.
This allows the entire chain complex to be treated as a functor.
A chain complex may then be defined as follows.
The boundary operator on a chain complex in homological algebra.
The chain complex is the central notion of homological algebra.
Dually, the boundary operators in a chain complex are sometimes called codifferentials.
The set of all k-chains forms a group and the sequence of these groups is called a chain complex.
See Homotopy category of chain complexes for further information.