## § Why terminal object is a limit

1. Thinking in Set, the terminal object is {*}, which is the empty product ofsets. Hence, the terminal is a type of product, which is a limit.
2. What does the terminal {*} project onto? It should project onto itscomponents, since its a limit. But recall that it was the limit of ZEROobjects. {*} vacuously projects into zero objects [ie, we're not obliged toconstruct a projection]
3. Think about products again. the product is universal such that any other"candidate for the product" must factor through a projection onto theproduct. Similarly, the terminal is universal such that any other "candidatefor the terminal" (literally all other objects) must factor through theterminal [ie, must map into the terminal].