HW9, due Wed Mar 22

  • Let F(A) and F'(A) both satisfy the universal property of a free group on a set A.  Show that there is a unique isomorphism from F(A) to F'(A) that is compatible with the canonical maps A -> F(A) and A -> F'(A).  Hint: consider the universal property for all possible combinations, taking both F(A) and F'(A) to be the free group and the supplementary group.
  • Can you see how a similar argument could be used to show quite generally that objects that satisfy universal properties are unique up to isomorphism?
  • DF 5.4 #2,
  • DF 5.4 #7,
  • DF 5.5 #23-a

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