713 Assignments for Fall 2015

  1. p.133 #1 -- "get-acquainted special"

  2. 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.

  3. 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.

  4. p.137 #4

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

  5. p.140 #1

  6. p.146 #4

  7. 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.

  8. p.153 #3

  9. p.520 #12

  10. p.162 #5

  11. Prove Thm.3 p.166.

  12. p.167 #6

    BONUS 2 p.167 #7

  13. p.170 #13.(b) and p.173 #4.(b)

  14. p.178 #4

  15. p.184 #2

  16. p.192 #1

  17. p.192 #4

  18. p.325 #1

  19. p.325 #6

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

  20. p.328 #3

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

  21. p.333 #2

  22. Prove that the coproduct in CRng is the tensor product.

  23. Determine the monics and epics in the category P of Assignment 1.

  24. p.511 #2

    BONUS 5 Find and verify all 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 .

    The remaining assignments are due Wed 9 Dec by 4:30 pm

    From the handout:

  25. p.1 #1, 2

  26. p.2 #1, 3


All rewrites of ungraded assignments
and any bonus problems
are due Mon 7 Dec by 4:30 pm.

Lists of assignments from Spring '13 and prior.


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