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 )