Math 726
Fall 2002
Exam 2
Due
Monday, November 18, 2002.
1.
Let
compute for the following
complexes A.
a)
A:= where the sequence is exact.
b)
A:= where for all
2.
If
is a family of
complexes written , then is defined as the
complex . Compute
3.
Show
that is an equivalence if
and only if is an isomorphism for
all
4.
Let
be an exact functor
from the category of modules to itself. If A is a complex, show that for all (What do you suppose
is meant by )