I read Maclane's book recently.
- the product of empty product is terminal object.this make sense if use the universal definition.
in the category of finite products(this is equivalent to any two objects of the category has product).the book has said it had terminal object. Just take the product of two empty objects.
I am confused about the following:
-take two empty object,this means in category $C$of finite products,we can consider empty object as an object of $C$. this make sense because empty object do not destroy the structure of any category.
- but if we consider the category of preorder $Z$($i\le j$ iff there is only one arrow from $i$ to $j$),then it has terminal object $+\infty$ and initial object $-\infty$.is this true?