= Solution
\b[Broadly in favour, if “trivial” means transparent once the correct structure has been identified.] The value of <category theory> is often to isolate a <universal property> that makes a repeated argument automatic.
For example, two objects with the same universal property have unique connecting maps in each direction. Their composites and the identities satisfy the same defining conditions, so uniqueness makes those composites identities. This one argument explains the uniqueness of <categorical products>, <categorical limits>, <adjoint functors> and many other constructions. It also specifies which isomorphism is canonical, a point that an arbitrary objectwise choice would miss.
The <Yoneda lemma> makes this perspective systematic. A <natural transformation> out of $\mathcal C(c,-)$ is determined by its value at $1_c$. Once that evaluation principle is recognized, questions about representable <functors> reduce to compositions in the original <category>. Similarly, the <Beck monadicity theorem> organizes many free-and-forgetful constructions around <monad algebras>, reflection of <isomorphisms> and specified <coequalizers>. The proof supplies a reusable explanation of why the algebraic structure can be reconstructed from the forgetful <functor>.
The substantial work lies in finding suitable definitions and verifying their hypotheses. The <Freyd general adjoint functor theorem>, for instance, needs completeness, local smallness and a solution set; none follows merely from calling a construction natural. The partial-operation tower below even has a <monadic length> that records how many distinct reconstruction steps are needed. These examples support the view that abstraction clarifies the source of an argument's simplicity. They also show why that simplicity is an achievement requiring proof.
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