# Tag Info

When people say "unique up to unique isomorphism" it must always be understood in the appropriate sense. This particular case is an instance of the uniqueness of objects defined by adjunctions. Suppose we have an adjunction $$F \dashv U : \mathcal{D} \to \mathcal{C}$$ where $F : \mathcal{C} \to \mathcal{D}$ is the left adjoint. Then, for each object $C$ in ...
Given a natural transformation of functors $\mathcal{C}' \to \mathcal{C}'$, say $h : f r \Rightarrow \mathrm{id}_{\mathcal{C}'}$ and a functor $f : \mathcal{C} \to \mathcal{C}'$, we can form a natural transformation $h f : f r f \Rightarrow f$ by taking the components of $h f$ at an object $c$ in $\mathcal{C}$ to be the component $h_{f c}$. You can view all ...