After completing a long proof in Category Theory or Module Theory, comparing one's work against a solution helps identify subtle logical gaps or "hand-waving" that a student might have overlooked. Conclusion
: A frequent error is assuming a group is Abelian or finite without the text explicitly stating so. solutions to abstract algebra dummit and foote
Let $G$ be a group and $a \in G$. Show that if $a^2 = e$, then $a = a^-1$. After completing a long proof in Category Theory