In summary, there exists another commutative diagram
For each [bar.[beta]] [member of] [[PI].sub.2]/[[GAMMA].sub.2] and [beta] [member of] [u.sup.-1.sub.2] ([bar.[beta]]), we have the following commutative diagram
through the morphism [J.sup.[infinity]] (50) and an A-module homomorphism [f.sup.[DELTA].sub.[infinity]] = [f.sup.[summation]] [omicron] [[pi].sup.[infinity].sub.k] (Example 16) in accordance with the commutative diagram
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the fuzzy hyperboloid, then the relation between the fuzzy folding [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the limit of the fuzzy retractions [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is discussed from the following commutative diagram
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 3.3 (a).
(d) This follows from the following commutative diagram
The commutative diagram
(2.1) implies that B[A.sup.r] = [A.sup.r]B.
Given an abelian category A assume that we have a commutative diagram
in A with exact lines:
(a-ii) G fixes a point not lying on C and there exists a commutative diagram
Given a k-string link f, the n-level group diagram for f, n [greater than or equal to] 2, is the commutative diagram
The former is trivial since the associated AHSS is strongly convergent and the latter (i.e., [Mathematical Expression Omitted]) follows from the commutative diagram