Structured chain complexes V
From Manifold Atlas
Let and
be chain maps and let
be a chain homotopy from~
to~
. Then the formula

gives another chain map making the following diagram commutative
![\displaystyle \xymatrix{C \ar[r]^{f} & D \ar[r]^{e} \ar[dr]_{g} & \mathcal{C}(f) \ar@{-->}[d]^{\Phi_j} \\ & & E }](/images/math/3/0/d/30db3c39d5fd27d72f99d239cd753f12.png)
Find appropriate for which we have

and
