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 )