A finite dimensional pointed algebra $A$ can be well understood via a finite directed graph (known as a quiver) by constructing an algebra from the quiver having $A$ as a well-behaved quotient. Jointly with John MacQuarrie we made the relationship between algebras and quivers functorial, obtaining an informative adjunction. This relationship passes to inverse limits, by considering "pseudocompact" quivers on one side and pseudocompact algebras on the other. Working with John MacQuarrie and Samuel Quirino, a similar adjunction is obtained for abstract quivers and arbitrary pointed coalgebras. This construction yields a different generalization to the pseudocompact case. I’ll explain all the main ideas involved.