- p.133 #1 -- "get-acquainted special"
- p.137 #4
BONUS p.133 #3 and p.137 #1
- 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.140 #1
- 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.
- p.146 #4
- p.153 #3
- 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.162 #5
- Prove Thm.3 p.166.
- p.167 #6
BONUS 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 Prove Prop.18 p.324 for f.g. free modules.
- p.328 #3
- p.333 #2
- p.334 #6
- p.337 #4
- Determine the monics and epics in the category P of Assignment
4.
- p.500 #4
- p.511 #2
BONUS Regard a group G as in Assignment 2. Prove that
an automorphism is inner if and only if it is naturally equivalent to
1G .
- p.516 #4--5
- p.520 #5.(b)
From the handout:
- p.1 #1
- p.1 #2 and p.2 #1, 3 -- due Mon 18 May by 4:30 pm
- p.3 #3, 4, 5 -- due Mon 18 May by 4:30 pm