interval object in chain complexes
Paths and cylinders
The standard interval object in a category of chain complexes in Mod is an “abelianization” of the standard simplicial interval, the 1-simplex and a model of the unit interval, , with the evident cell decomposition.
Let be some ring and let Mod be the abelian category of -modules. Write for the corresponding category of chain complexes.
The standard interval object in chain complexes
is the normalized chain complex of the simplicial chains on the simplicial 1-simplex:
In components this means that
See the entry on chain homotopy for more details.
Revised on September 3, 2012 13:21:36
by Tim Porter