limit

• a limit of diagram $F: D \to C$ in a category $C$ is
  • an object $\text{lim}\ F$ of $C$ equipped with morphisms to the objects $F(d)$ for all $d \in D$
  • such that everything in sight commutes
  • Moreover, it is the universal object with the property that
    • it is the “most optimized solution” to the problem of finding such thing
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