713 Assignments for Spring 2013

  1. Consider the set P of all positive integers. Define an arrow from to if and only if divides . Show that this provides the structure of a (non-concrete) category on the positive integers. -- "get-acquainted special"

  2. p.133 #1

  3. p.137 #4

  4. 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.

    BONUS 1 p.133 #3 and p.137 #1

  5. p.140 #1

  6. p.146 #4

  7. p.153 #3

  8. 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.

  9. p.162 #5

  10. Prove Thm.3 p.166.

  11. p.167 #6

    BONUS 2 p.167 #7

  12. p.178 #4

  13. p.184 #2

  14. p.192 #1

  15. p.192 #4

  16. p.325 #1

  17. p.325 #6

    BONUS 3 Prove Prop.18 p.324 for f.g. free/projective modules.

  18. p.328 #3

    BONUS 4 Same for f.g. free/projective modules.

  19. p.333 #2

  20. p.334 #6

  21. Determine the monics and epics in the category P of Assignment 0.

  22. p.500 #4

  23. p.511 #2

  24. Show that the isomorphisms in (35) p.181 and (32) p.321 are natural in ModK.

    BONUS 5 Find and verify all other natural isomorphisms in ModK from Chapters V and IX.8--12.

    BONUS 6 Regard a group as in Assignment 2. Prove that an automorphism is inner if and only if it is naturally equivalent to 1G .

  25. p.516 #4--5

  26. p.520 #4

  27. p.520 #5.(b)

  28. p.520 #12

    From the handout:

  29. p.1 #1

  30. p.1 #2 -- due Fri 3 May

    The remaining assignments are due Wed 15 May by 4:50 pm

  31. p.2 #1, 3

  32. p.3 #3, 4, 5


All rewrites of ungraded assignments
and any bonus problems
are due Wed 8 May by 4:50 pm.

Lists of assignments from Spring '11 and prior.


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