Relative cell complex
= Relative cell complex
{title2=$X=Z_0\to Z_1\to\cdots\to Z_\infty$}
A composite built by successive pushouts of coproducts of prescribed generating maps. In nonnegative chain complexes, attaching a sphere-to-disk generator adds a free element with a specified existing cycle as boundary. The resulting inclusion has a degreewise free cokernel.