- p.133 #1 -- "get-acquainted special"
- Consider the set
**P**of all positive integers. Define an arrow from*m*to*n*if and only if*m*divides*n*. Show that this provides the structure of a (non-concrete) category on the positive integers. - Prove that a group is a (non-concrete) category with one object in
which all arrows are invertible, and that a morphism of groups is a functor
of such categories.
- p.137 #4
BONUS 1 p.133 #3 and p.137 #1

- p.140 #1
- p.146 #4
- Prove that a lattice is a category in which any two objects have at
most one arrow between them, and that has products and coproducts.
- p.153 #3
- p.520 #12
- p.162 #5
- Prove Thm.3 p.166.
- p.167 #6
BONUS 2 p.167 #7

- p.170 #13.(b) and p.173 #4.(b)
- p.178 #4
- p.184 #2
- p.192 #1
- p.192 #4
- p.325 #1
- p.325 #6
BONUS 3 Prove Prop.18 p.324 for f.g. free/projective modules.

- p.328 #3
BONUS 4 Same for f.g. free/projective modules.

- p.333 #2
- Prove that the coproduct in
**CRng**is the tensor product. - Determine the monics and epics in the category
**P**of Assignment 1. - p.511 #2
BONUS 5 Find and verify all natural isomorphisms in

*Mod*from Chapters V and IX.8--12._{K}BONUS 6 Regard a group

*G*as in Assignment 2. Prove that an automorphism is inner if and only if it is naturally equivalent to 1_{G}.**The remaining assignments are due Wed 9 Dec by 4:30 pm**From the handout:

- p.1 #1, 2
- p.2 #1, 3

and any bonus problems

are due Mon 7 Dec by 4:30 pm.