Every limit starts with a diagram. It is sometimes given by a little category $J$ and a functor from $J$ into $C$ that picks out the diagram. For a Cartesian product, say in Set, what is this diagram? Is it just two objects and no arrows?
2026-03-28 22:36:55.1774737415
What is the diagram for the limit that is the Cartesian product?
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Yes, two objects with no arrows is exactly the diagram that gives you the product as a limit.