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\begin{document}

\title[101 Homework \#29]{Math 101: Graduate Linear Algebra \\ Homework, Day \#29}
\date{Assigned Friday, 10 November 2017; due Monday, 13 November 2017}

\maketitle

\vspace{1ex}

\begin{problab}{29.1} 
Show that a group can be considered as a category with one object in which all morphisms are isomorphisms, and vice versa.
\end{problab}

\begin{problab}{29.2} 
Show that the association $R \mapsto R^\times$ defines a functor from the category of rings to the category of groups.  Show by explicit examples that this functor is neither faithful nor full.
\end{problab}

\end{document}