A chain map is a homomorphism of chain complexes. Chain complexes with chain maps between them form the category of chain complexes.
Let be two chain complexes in some ambient additive category (often assumed to be an abelian category).
A chain map is a collection of morphism in such that all the diagrams
commute, hence such that all the equations
For a chain map, it respects boundaries and cycles, so that for all it restricts to a morphism
In particular it also respects chain homology
In fact this is a universal delta-functor.
A basic discussion is for instance in section 1.1 of
A more comprehensive discussion is in section 11 of
Revised on September 2, 2012 20:28:57
by Urs Schreiber