8]), we need the following commutative diagram
similar to the diagram in Section 3.
If M is an A-G-module where G acts rationally on A and M is a rational G-module, finitely generated as an A-module, then an A-free (projective) resolution of M can be lifted to an A-G-free resolution, that is a commutative diagram
These three isometries form the commutative diagram
in Figure 3.
It is clear from the commutative diagram
(30) that the equivalence P sends relative projectives into relative projective; similarly, it is clear from the commutative rectangle (31) that relative injectives are sent by an equivalence into relative injectives.
Given an abelian category A assume that we have a commutative diagram
in A with exact lines:
we have the following commutative diagram
of (compact) topological groups with exact rows
greater than or equal to]8](K), we have a commutative diagram
Mathematical Expression Omitted]) follows from the commutative diagram
summation of^K, of sufficiently high power, there is a commutative diagram
Suppose we are given any homotopy commutative diagram
Then we obtain a commutative diagram
of exact sequences
11] Consider a commutative diagram
of unbroken arrows: